It is commonly quoted that any two humans are identical at 99.9% of their three billion DNA letters. However, this statement also means that there are roughly three million positions where any two genomes are different. Many such variants have been accumulating throughout hundreds of thousands of years of human evolution and provide a record of human history. Additionally, many of these variants acting together will affect how many children an individual will have or may contribute to the risk of common diseases. Here I will describe two projects aimed at learning about human history and natural selection from genetic variation data. First, through the analysis of genetic variation in the coding regions of genes obtained from 1500 Han Chinese and Danish individuals, I find evidence for extreme, recent, population growth in both populations. However, this growth appears to have been greater in the Han Chinese than in the Danes. The second project is based on the analysis of genetic diversity on the human Y chromosome. We find that genetic diversity is substantially lower than expected on this chromosome. Sex-biased demographic processes throughout human history cannot, by themselves, explain this reduction in genetic diversity. Rather, natural selection removing deleterious mutations from nearly 4Mb of the Y chromosome, or natural selection increasing the frequency of beneficial mutations is required to explain the data.