The increasing prevalence of dementia presents significant challenges for healthcare, and Socially Assistive Robots (SARs) have emerged as a promising solution to support cognitive training and assist therapists in eldercare. This chapter aims to address several key questions as part of our primary goal: the development of a fully autonomous robot for delivering cognitive training. Within this scope, personalisation is tackled by developing robots that are both adaptable, allowing therapists to customise their high-level behaviour, and adaptive, enabling real-time adjustments to meet users’ evolving needs. This monograph takes a therapist-oriented approach to develop a fully autonomous SAR for cognitive training, ensuring that the expertise of healthcare professionals informs the system’s design and functionality. It explores the impact of human-like characteristics-such as personality, communication style, and backchanneling-on user engagement and task performance, while also investigating AI-driven reasoning techniques that enable SARs to learn and optimise socially assistive behaviours tailored to individual abilities.