Although thousands of genomic regions have been associated with heritable human diseases, attempts to elucidate biological mechanisms are impeded by a general inability to discern which genomic positions are functionally important. Evolutionary constraint is a powerful predictor of function that is agnostic to cell type or disease mechanism. Here, single base phyloP scores from the whole genome alignment of 240 placental mammals identified 3.5% of the human genome as significantly constrained, and likely functional. We compared these scores to large-scale genome annotation, genome-wide association studies (GWAS), copy number variation, clinical genetics findings, and cancer data sets. Evolutionarily constrained positions are enriched for variants explaining common disease heritability (more than any other functional annotation). Our results improve variant annotation but also highlight that the regulatory landscape of the human genome still needs to be further explored and linked to disease.