This article gives an overview of the literature on asset management for multi-unit systems with an emphasis on two multi-asset categories: fleet (a system of homogeneous assets) and portfolio (a system of heterogeneous assets). As asset systems become more complicated, researchers have employed different terms to refer to their specific problems. With an objective to facilitate readers in searching conducive studies to their interests, this paper establishes a novel classification scheme for multi-unit systems in accordance with essential features such as diversity of assets and intervention options. Moreover, discerning differences in characteristics between cross-component and cross-asset interactions, we select three types of potential multi-component dependencies (performance, stochastic, and resource) and extend their notions to be applicable to multi-asset systems. The investigation into these dependencies enables the identification of problems that could exist in real industrial settings but are yet to be determined in academia. Ultimately, we delve into modelling approaches adopted by previous researchers. This comprehensive information allows us to offer the insights into the current trends in multi-asset maintenance. We expect that the output of this review paper will not only stress research gaps on multi-asset systems, but more importantly help systematise future studies on this aspect.