Cellular metabolism generates molecular damage affecting all levels of biological organization. Accumulation of this damage over time is thought to play a central role in the aging process, but damage manifests in diverse molecular forms complicating its assessment. Insufficient attention has been paid to date to the role of molecular damage in aging-related phenotypes, particularly in humans, in part because of the difficulty in measuring its various forms. Recently, omics approaches have been developed that begin to address this challenge, because they are able to assess a sizeable proportion of age-related damage at the level of small molecules, proteins, RNA, DNA, organelles and cells. This review describes the concept of molecular damage in aging and discusses its diverse aspects from theoretical models to experimental approaches. Measurement of multiple types of damage enables studies of the role of damage in human aging outcomes and lays a foundation for testing interventions to reduce the burden of molecular damage, opening new approaches to slowing aging and reducing its consequences.