Over 180 million years since their divergence from autosomes, mammalian Y chromosomes have evolved a gene repertoire highly specialized for male reproduction. Y chromosomes are also a valuable tool for population genetics and phylogeny because they are inherited without recombination from a single parent. The Y chromosome of the house mouse (Mus musculus) is exceptional in that it is almost entirely euchromatic and has important roles in speciation. However, its complex repetitive structure has hindered analyses by high-throughput sequencing. We sought to fill this gap by performing a systematic survey of Y-linked variation in mouse. We have compiled whole-genome sequencing data for 132 male samples including wild-caught and laboratory representatives of each of the three subspecies of the house mouse (Mus musculus domesticus, M. m. musculus and M. m. castaneus) and transcriptome data from outgroup specices. First, we show that both the short and long arms of the Y chromosome of the three subspecies are differentiated by megabase-sized structural variants. Next we apply several complementary approaches to obtain a catalog of sequence variants in the non-ampliconic portion of the Y chromosome. Using laboratory strains with known pedigree relationships, we estimate the average mutation rate on Y to be 9.1 ± 1.8 × 10-9 per site per generation. Finally we use approximate Bayesian computation to compare patrilineal and matrilineal demographic patterns in wild mice. We find evidence for increased geographic differentiation and reduced effective population size on the Y compared to the mitochondria, and attribute this to the combined effects of background selection and variability in male reproductive success.