Genomic alterations driving tumorigenesis result from the interaction of environmental exposures and endogenous cellular processes. With a diversity of risk factors, liver cancer is an ideal model to study these interactions. Here, we analyze the whole genomes of 44 new and 264 published liver cancers and we identify 10 mutational and 6 structural rearrangement signatures showing distinct relationships with environmental exposures, replication, transcription, and driver genes. The liver cancer-specific signature 16, associated with alcohol, displays a unique feature of transcription-coupled damage and is the main source of CTNNB1 mutations. Flood of insertions/deletions (indels) are identified in very highly expressed hepato-specific genes, likely resulting from replication-transcription collisions. Reconstruction of sub-clonal architecture reveals mutational signature evolution during tumor development exemplified by the vanishing of aflatoxin B1 signature in African migrants. Finally, chromosome duplications occur late and may represent rate-limiting events in tumorigenesis. These findings shed new light on the natural history of liver cancers.