This chapter describes the state of the art of Socially Assistive Robots on the topics dealt with in this monograph. The first part explores the adaptable pillar that enables humans to customise and personalise robots in an easy and intuitive way and based on specific robot’s human-like characteristics, such as personality, backchannelling, and communication style. On the other hand, the second part discusses the current techniques developed for enabling robots to be adaptive, that is, reason and make the correct decision according to the user’s profile, needs, and preferences. The chapter concludes by describing the set of requirements defined by the therapists for the use-case of this monograph, namely, cognitive training therapy for Persons with Dementia.