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Affect recognition is an interdisciplinary research field bringing together researchers from natural and social sciences. Affect recognition research aims to detect the affective state of a person based on observables, with the goal to, for example, provide reasoning for the person’s decision making or to support mental wellbeing (e.g., stress monitoring). Recently, beside of approaches based on audio, visual or text information, solutions relying on wearable sensors as observables, recording mainly physiological and inertial parameters, have received increasing attention. Wearable systems enable an ideal platform for long-term affect recognition applications due to their rich functionality and form factor, while providing valuable insights during everyday life through integrated sensors. However, existing literature surveys lack a comprehensive overview of state-of-the-art research in wearable-based affect recognition. Therefore, the aim of this paper is to provide a broad overview and in-depth understanding of the theoretical background, methods and best practices of wearable affect and stress recognition. Following a summary of different psychological models, we detail the influence of affective states on the human physiology and the sensors commonly employed to measure physiological changes. Then, we outline lab protocols eliciting affective states and provide guidelines for ground truth generation in field studies. We also describe the standard data processing chain and review common approaches related to the preprocessing, feature extraction and classification steps. By providing a comprehensive summary of the state-of-the-art and guidelines to various aspects, we would like to enable other researchers in the field to conduct and evaluate user studies and develop wearable systems.