In the course of discovering the first mutagen (X-rays) just over 60 years ago, Herman J. Muller asked whether X-rays induced single-gene mutations and/or chromosomal (multiple-gene) mutations. To a large extent, his question has set the agenda for mutagenesis research ever since. We explore historically the answers to this question, with special emphasis on recent developments in the field of mammalian cell mutagenesis. Studies indicate that ionizing radiation and many chemical mutagens/carcinogens induce both gene and chromosomal mutations; however, only certain genetic systems permit the recovery and analysis of both classes of mutations. Few chemical mutagens induce only gene mutations in mammalian cells; instead, most mutagens appear to induce both classes of mutations, with chromosomal mutations (especially multilocus deletions) predominating at high doses. These results have implications regarding the mechanisms of mutagenesis, the role of chromosomal mutations in carcinogenesis and hereditary disease, and the type of data required for risk assessment of physical and chemical mutagens/carcinogens.