Abstract

Most selection in humans seem to be soft sweeps.
More classical hard sweeps are found in non-Africans. 

Main Text

When most people think of evolutionary biology what they think of is adaptation, as in Charles' Darwin's On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life[1]​.
Arguably this precedent by Charles Darwin where adaptation took center stage crested in the mid-20th century with the "Modern Synthesis.[2]​" But often reactions elicit counter-reactions, and for the past few generations there has been a shift away from this adaptationist framework.
Though Richard C.
Lewontin and Stephen Jay Gould's The spandrels of San Marco and the Panglossian paradigm: a critique of the adaptationist programme[3]​ probably has made the public familiar with the counter-narrative, within evolutionary biology the "neutral model" as inferred from molecular data has arguably been much more influential[4]​. 
Within population genetics there is a focus upon the parameters of the underlying phenomena which drive change in allele frequency.
Though natural selection upon heritable variation is one of those drivers of change in allele frequency, results from molecular patterns of variation in the 1960s indicated that selection was not the primary driver of polymorphism.
Rather, random drift in concert with mutation may have operated together to maintain an equilibrium state of variation.
Without such a strong focus on selection the tendency toward conceptualizing evolution as a contingent, and random, process, became more prominent.
One can see this in the debates between Stephen Jay Gould, who argued for historical contingency[5]​, and his opponents, including Richard Dawkins[6]​ and Simon Conway Morris[7]​.
These sorts of debates lend prominence to scholars with a literary flair, and frankly in the case of both Gould and Dawkins a "gift for gab" and self-promotion.
But verbal volleys flourish, even proliferate, most in the absence of dispositive data.
In regards to evolutionary genetics, which has become evolutionary genomics, we no longer live in such a data poor a world. Gottfried Wilhelm Leibniz[8]​ naively dreamed in the 17th century that arguments could be resolved by the maxim "let us calculate." Within the field of evolutionary genetics we are far closer to realizing that dream, and burying tired old debates, than we were a generation ago.
No longer are biologists arguing about the reasons why selection or random genetic drift should be dominant, they are collecting the data from the various branches of the tree of life and attempting to adduce the overall shape of things.
To paraphrase Leibniz, "let us estimate."
Because of the surfeit of data we are now able to obtain a scenario where we won't always necessarily make recourse to a naive null hypothesis of neutrality.
Instead of testing the shape of reality against preconceptions, we can actually attempt to sketch it out based on the data on hand.
To give a general flavor of the resurgence of a selectionist viewpoint, driven by data rather than prior preconceptions, I would point you to Enard et al.
2014[9]​, Genome-wide signals of positive selection in human evolution:
The role of positive selection in human evolution remains controversial.
On the one hand, scans for positive selection have identified hundreds of candidate loci, and the genome-wide patterns of polymorphism show signatures consistent with frequent positive selection.
On the other hand, recent studies have argued that many of the candidate loci are false positives and that most genome-wide signatures of adaptation are in fact due to reduction of neutral diversity by linked deleterious mutations, known as background selection...Our results suggest that adaptation was frequent in human evolution and provide support for the hypothesis of King and Wilson that adaptive divergence is primarily driven by regulatory changes.
I do not believe that it will be long before we will have a "one-handed" biologist, though what is within that hand may be taxon specific.
Enard et al.'s paper is not the final word, rather, it is part of a continuing discussion, enriched by data, and converging upon broad general inferences.
So far I have spoken of selection at the highest level.
But selection is just a term which we humans use to bracket a set of related phenomena with their own subtleties.
There is for example negative and positive selection, which eliminates deleterious alleles or increases the frequencies of favored ones.
Balancing selection maintains variation, genetic polymorphism, through various dynamics such as frequency dependent selection, selection varying due to special or temporal heterogeneity, and heterozygote advantage.
These categories of selection are focused on the role of the process in changing allele frequencies over time, the sine qua non of evolutionary process from a genetic perspective.
But with genomics researchers can now look at even more detail as to the dynamics, and implicitly constraints, of evolutionary process, by inspecting patterns across the genome.
In an idealized population genetic model one can draw upon infinite variation to increase fitness in changing environments.
In the real world of DNA sequences variation is finite, and subject to population genetic forces such as drift (which generally reduces variation) and mutation (which increases variation). 
Within this context positive selection can be soft, or it can be hard.
What does this mean? As a stylized concept "hard selection" operates upon novel singular mutations.
In contrast, "soft selection" operates genetic variation which is already prevalent within the population.
The population genomic methods pioneered in the decade of the 2000s were optimized for detecting hard selection events.
Basically new variants which in a singular fashion swept away diversity across vast flanking regions of the genome in a homogeneous manner.
One can imagine why these sorts of events were easy to detect (albeit with a non-trivial false positive risk).
But, one must not confuse limitations of perception and detection for the true nature of reality.
Ultimately the mirror through which we look darkly has become progressively more transparent over time, and because of increased marker density and sample size, basically the increase in data generation of genomics and analytic power of modern computation, we can can detect much more subtle selection events.
Over the past 10 years or so there has been a vogue for a genome-of-the-week papers (more recently, obscure genome-of-the-day papers which purport to shed light on cancer).
These are brute force analyses.
Paint-by-numbers science.
True, they may shed light on stark and striking patterns of differentiation or parallelism between single genomes of various species, but often these are the true but trivial category, or novel but dubious.
A newer and less well known domain of study focuses on deeper, more precise, analyses of subtle variations within species.
This is the sort of work necessary for anyone attempting to understand the role of microevolutionary processes and how they shape genetic and ultimately morphological variation, and the broad sweep of evolution writ large.
The one billion year view may suggest to you that evolution is "substrate neutral," but dynamical details of the substrate constrain the path from A to Z within historical time to a finite set of channels.
In this vein, a preprint came to my attention a few months back which I think shows us a likely pathway forward in terms of evolutionary genetic illumination, Soft sweeps are the dominant mode of adaptation in the human genome[10]​:
The degree to which adaptation in recent human evolution shapes genetic variation remains controversial.
This is in part due to the limited evidence in humans for classic “hard selective sweeps,” wherein a novel beneficial mutation rapidly sweeps through a population to fixation.
However, positive selection may often proceed via “soft sweeps” acting on mutations already present within a population.
Here we examine recent positive selection across six human populations using a powerful machine learning approach that is sensitive to both hard and soft sweeps.
We found evidence that soft sweeps are widespread and account for the vast majority of recent human adaptation. Surprisingly, our results also suggest that linked positive selection affects patterns of variation across much of the genome, and may increase the frequencies of deleterious mutations.
Our results also reveal insights into the role of sexual selection, cancer risk, and central nervous system development in recent human evolution.
[Fig 1]​Ultimately you can't understand this madness without the method.
A previous paper in PLOS GENETICS, S/HIC: Robust Identification of Soft and Hard Sweeps Using Machine Learning[11]​, is highly useful to read to understand the results above (or at least how they were obtained).
Obviously I recommend you read the whole paper, but basically the method takes a whole bunch of summary statistics generated by other techniques to detect various types of selection, and explores how those statistics vary across segments of the genome conditional upon the type of selection (in additional to non-selective events and dynamics which shape or constrain genetic variation, which in the case of humans is often a matter of demographics).
In this way the technique "understands" the patterns which are likely indicative of hard vs.
soft selection.
What did they detect? First, a whole lot of sweeps in their data set of genetically distinct 1000 Genomes populations.
Nearly ~2,000 sweeps.
190 were in all six of their study populations (YRI, GWD, LWK, CEU, JPT, and PEL), indicative to me of some sort of balancing going on here (or very old and slow sweeps?).
59 sweeps were shared by African populations, and 71 by non-Africans.
Remember here that these Africans diverged from non-Africans on the order of ~100,000 years ago, while the non-Africans diversified ~50,000 years ago.
Also, the African groups here share common ancestry in the Holocene from what I know, in particular the YRI and LWK.
So the overlap across African groups is not entirely surprising to me. 
Over 90% of the sweeps they detected were soft, and non-Africans tended to be much more likely to exhibit signatures of hard sweeps.
This makes sense to me, insofar as non-Africans lost a fair amount of diversity after they left Africa, and, they were likely subject to novel selective pressures and had to adapt rather rapidly.
What I have a harder time comprehending is how seriously to take their huge number of detected sweeps, though this result was anticipated by other research groups[12]​.
There is an allusion to false positives, but I don't have a good sense of what proportion of the nearly 2,000 hits are true hits.
The fact that their sweeps are found more often in coding regions does indicate though they're picking up a lot of selection driving by functionally relevant adaptations.
Their results also seem to suggestion that these sweeps increase frequencies of some deleterious alleles due to linked selection.
This seems predictable and reasonable with such a high number of selection events.
All in all the copiousness of selection seems to align well with the recent results coming out of Jonathan Pritchard's lab[13]​.
Though to be honest I am not entirely sure that the Pritchard lab's method is not some artifact, as some of the world-wide patterns are so similar as to strike me as action-at-a-distance level of suspicious.
Finally there's an extensive laundry list of genes which may be targets of selection, and how that makes biological sense.
To digest such lists takes more time and energy than I have now, though if you are a gene-jockey with a love for a particular locus (you know who you are) I invite you to invoke your "control-f" privileges. I would suggest though that the mention in the abstract of "sexual selection" doesn't really have a payoff.
I don't think most people are thinking about sperm competition when they think of sexual selection, though I see where this comes from.
The overall conclusion that most selection in humans in soft selection is plausible.
I don't know if it's true, but I think it probably is true. Most human traits which vary exhibit a polygenic genetic architecture, with lots of small effect quantitative trait loci.
Selection won't yield genomic signatures which are similar to hard sweeps.
But certainly selection is operating upon these quantitative phenotypes.
And what is true for humanity, I think is likely true for the tree of life more broadly.
Most selection will turn out to be softer than we'd imagined.
The data will tell us soon enough.