Here we ask the question "How much information do epigenomic datasets provide about human genomic function?" We consider nine epigenomic features across 115 cell types and measure information about function as a reduction in entropy under a probabilistic evolutionary model fitted to human and nonhuman primate genomes. Several epigenomic features yield more information in combination than they do individually. We find that the entropy in human genetic variation predominantly reflects a balance between mutation and neutral drift. Our cell-type-specific FitCons scores reveal relationships among cell types and suggest that around 8% of nucleotide sites are constrained by natural selection.