The shift in research focus from Industry 4.0 to Industry 5.0 (I5.0) promises a human-centric workplace, with social and well-being values at the centre of technological implementation. Human-Robot Collaboration (HRC) is a core aspect of I5.0 development, with an increase in adaptive and personalised interactions and behaviours. This review investigates recent advancements towards personalised HRC, where user-centric adaption is key. There is a growing trend for adaptable HRC research, however there lacks a consistent and unified approach. The review highlights key research trends on which personal factors are considered, workcell and interaction design, and adaptive task completion. This raises various key considerations for future developments, particularly around the ethical and regulatory development of personalised systems, which are discussed in detail.