In personalized machine learning, the aim of personalization is to train a model that caters to a specific individual or group of individuals by optimizing one or more performance metrics and adhering to specific constraints. In this paper, we discuss the need for personalization in affective computing and present the first survey of existing approaches for personalization in affective computing. Our review spans training techniques and objectives towards the personalization of affective computing models across various interaction modes and contexts. We develop a taxonomy that clusters existing approaches into Data-level and Model-level approaches. Across the Data-Level and Model-Level broad categories, we group existing approaches into seven sub-categories: (1) User-Specific Models, (2) Group-Specific Models, (3) Weighting-Based Approaches, (4) Feature Augmentation, (5) Generative-Based Models which fall into the Data-Level approaches, (6) Fine-Tuning Approaches, and (7) Multitask Learning Approaches falling under the model-level approaches. We provide a problem formulation for personalized affective computing, and to each of the identified sub-categories. Additionally, we provide a statistical analysis of the surveyed literature, analyzing the prevalence of different affective computing tasks, interaction modes (i.e. Human-Computer Interaction (HCI), Human-Human interaction (HHI), Human-Robot Interaction (HRI)), interaction contexts (e.g. educative, social, gaming, etc.), and the level of personalization among the surveyed works. Based on our analysis, we provide a road-map for researchers interested in exploring this direction.