Neanderthals accumulated 40% higher deleterious mutation load than humans due to population bottleneck. Non-Africans inherited Neanderthal weakly deleterious alleles reducing fitness by at least 0.5%. Africans have lower mutation load without Neanderthal admixture. Neanderthal DNA depleted near genes by selection against deleterious load, not epistasis. Initial Neanderthal admixture up to 10% purged mostly in first 20 generations if additive effects. Recessive mutations cause positive selection for Neanderthal haplotypes masking human recessives. Neanderthal fitness 0.63 of humans if additive, 0.39 if recessive. Weakly deleterious mutations with s=5e-5 to 2e-3 accumulated more in Neanderthals. Out-of-Africa bottleneck plus Neanderthal admixture each reduce non-African fitness by 1%. Neanderthal load explains genome-wide depletion patterns without reproductive incompatibilities. Denisovans likely imposed similar load on admixed Asians and Oceanians. Neanderthal exome shows weaker purifying selection than humans. Bottleneck lasted 10 times longer in Neanderthals. Surviving Neanderthal alleles affect polygenic traits more than Mendelian diseases. Heterosis from recessive effects increased admixture from 1% to 3% over time. Background selection reduces Neanderthal ancestry over 1Mb around deleterious sites. Non-Africans' excess weak load persists due to common variants.