There is long-standing interest in nonaqueous uranium chemistry because of fundamental questions about uranium’s variable chemical bonding and the similarities of this pseudo-Group 6 element to its congener d-block elements molybdenum and tungsten. To provide historical context, with reference to a conference presentation slide presented around 1988 that advanced a defining collection of top targets, and the challenge, for synthetic actinide chemistry to realize in isolable complexes under normal experimental conditions, this Viewpoint surveys progress against those targets, including (i) CO and related π-acid ligand complexes, (ii) alkylidenes, carbynes, and carbidos, (iii) imidos and terminal nitrides, (iv) homoleptic polyalkyls, -alkoxides, and -aryloxides, (v) uranium–uranium bonds, and (vi) examples of topics that can be regarded as branching out in parallel from the leading targets. Having summarized advances from the past four decades, opportunities to build on that progress, and hence possible future directions for the field, are highlighted. The wealth and diversity of uranium chemistry that is described emphasizes the importance of ligand–metal complementarity in developing exciting new chemistry that builds our knowledge and understanding of elements in a relativistic regime.