First, a few definitions.
Evolution can be defined as the change in "allele frequencies" over time, where "allele frequency" can e.g. be "how often does mutation X occur in this population", or "what fraction of the population has double the copies of gene X".
This evolution can be both adaptive and non-adaptive.
Adaptive changes in allele frequencies are those that respond to selective pressure, i.e. these changes modify the organism such that it responds either better (positive selection) or worse (negative selection) to the environment, and is thus able to have more, or fewer viable offspring, respectively. This change in viable offspring is usually called "natural selection", though the same mechanisms apply for breeding.
Non-adaptive changes in allele frequencies are those that occur regardless of any selective pressure. These include random mutations, genetic drift (i.e. changes in allele frequencies that happen by chance, and are often slightly deleterious), and recombination (the choice of which alleles you get from which grandparent).
When people claim that "evolution is slowing down", they usually mean that there is less adaptive evolution. Before I go into that, let's quickly look at non-adaptive evolution. There would be two ways how non-adaptive evolution could slow down: Either, we are exposed to fewer mutagens, i.e. chemicals or radiation that leads to mutations. This is most likely not the case. Alternatively, non-adaptive evolution could be slowed down if we started reproducing clonally, which hasn't happened yet. In sum, non-adaptive evolution has not slowed down, and may even be speeding up.
The speed of adaptive evolution depends on two factors (see e.g. here): The strength of the positive or negative effect of the allele, and the size of the population. Due to non-adaptive effects, such as mutation, which can revert a beneficial allele modification, or recombination, which can prevent the allele from propagating, there is always some "noise" when passing on alleles to the next generation. Averaged over an entire population, this noise is a lot more important when the population is small than when the population is big. Alleles whose effect is weaker than the noise level will not be selected for, because they'll simply disappear again. Thus, as population size increases, more and more alleles will have a noticeable positive or negative effect, and will thus be selected for or against.
In other words, as the number of humans increases, adaptive evolution should speed up. This prediction has been shown to be true for humans in the last 40k years. However, this study could only look up to some 5-10k year ago, since not enough genome data was available at the time.
So is it possible that since then, speed of adaptive evolution has slowed down? Clearly, the human population size is expanding, so we would expect that this speed-up effect should be still present today. What we can influence thanks to e.g. modern medicine is the selective pressure, i.e. there is less positive and negative selective pressure on some alleles than before. Thus, for certain specific features, adaptive evolution might in fact have slowed down, if the strength of the selection effect has decreased more than the effect of increased population size. At the same time, there are plenty of new environmental challenges for our bodies - for example, it is now quite beneficial to have a genetic makeup that allows you to respond well to mainstream drugs, and, as @Christian has mentioned, there is now the possibility of genetic screening combined with safer abortions that is already changing the male/female ratio.
In conclusion, non-adaptive evolution is possibly speeding up, and adaptive evolution is most likely speeding up as well - it's just still not as fast that people see effects within a handful of generations.