Substances of unknown or variable composition, complex reaction products, or biological materials (UVCBs) are over 70 000 "complex" chemical mixtures produced and used at significant levels worldwide. Due to their unknown or variable composition, applying chemical assessments originally developed for individual compounds to UVCBs is challenging, which impedes sound management of these substances. Across the analytical sciences, toxicology, cheminformatics, and regulatory practice, new approaches addressing specific aspects of UVCB assessment are being developed, albeit in a fragmented manner. This review attempts to convey the "big picture" of the state of the art in dealing with UVCBs by holistically examining UVCB characterization and chemical identity representation, as well as hazard, exposure, and risk assessment. Overall, information gaps on chemical identities underpin the fundamental challenges concerning UVCBs, and better reporting and substance characterization efforts are needed to support subsequent chemical assessments. To this end, an information level scheme for improved UVCB data collection and management within databases is proposed. The development of UVCB testing shows early progress, in line with three main methods: whole substance, known constituents, and fraction profiling. For toxicity assessment, one option is a whole-mixture testing approach. If the identities of (many) constituents are known, grouping, read across, and mixture toxicity modeling represent complementary approaches to overcome data gaps in toxicity assessment. This review highlights continued needs for concerted efforts from all stakeholders to ensure proper assessment and sound management of UVCBs.