The prevalence of highly repetitive sequences within the human Y chromosome has led to its incomplete assembly and systematic omission from genomic analyses. Here, we present long-read de novo assemblies of 43 diverse Y-chromosomes, three contiguously assembled including two from deep-rooted African Y lineages. Examination of the full extent of genetic variation between Y chromosomes across 180,000 years of human evolution reveals its remarkable complexity and diversity in size and structure, in contrast with its low level of base substitution variation. The size of the Y chromosome assemblies vary extensively from 45.2 to 84.9 Mbp, with individual repeat arrays showing up to 6.7-fold difference in length across samples. Half of the male-specific euchromatic region is subject to large (up to 5.94 Mbp) inversions with a >2-fold higher recurrence rate compared to the rest of the human genome. The Y centromere, composed of 171 bp α-satellite monomer units, appears to have evolved from tandem arrays of a 36-mer ancestral higher order repeat (HOR), which has been predominantly replaced by a 34-mer HOR, and reveals a pattern of higher sequence variation towards the short-arm side. The Yq12 heterochromatic region is ubiquitously flanked by approximately 649 kbp and 472 kbp inversions that maintain the alternating arrays of DYZ1 and DYZ2 repeat units in between. While the sizes and the distribution of the DYZ1 and DYZ2 arrays vary considerably, primarily due to local expansions and contractions, the copy number ratio between the DYZ1 and DYZ2 monomer repeat units remains consistently close to 1:1. In addition, we have identified on average 65 kbp of novel sequence per Y chromosome. The availability of sequence-resolved Y chromosomes from multiple samples provides a basis for identifying new associations of specific traits with the Y chromosome and garnering novel evolutionary insights.