Two types of physical maps are described: restriction maps made by top down approaches using enzymes that cut the genome infrequently, and complete libraries, made by bottom up approaches using fingerprinting of randomly selected cloned DNA. Construction of such maps for mammalian chromosomes is complicated by the mosaic nature of mammalian genomes, and extensive polymorphisms at the cleavage sites of most enzymes that yield large DNA fragments. However, it appears that both of these potential difficulties can be turned into advantages by new mapping strategies. When combined with yeast artificial chromosome cloning and polymerase chain reaction amplification methods, these approaches should soon yield complete maps of many human chromosomes.