The seminal work on Affective Computing in 1995 by Picard set the base for computing that relates to, arises from, or influences emotions. Affective computing is a multidisciplinary field of research spanning the areas of computer science, psychology, and cognitive science. Potential applications include automated driver assistance, healthcare, human-computer interaction, entertainment, marketing, teaching and many others. Thus, quickly, the field acquired high interest, with an enormous growth of the number of papers published on the topic since its inception. This paper aims to (1) Present an introduction to the field of affective computing though the description of key theoretical concepts; (2) Describe the current state-of-the-art of emotion recognition, tracing the developments that helped foster the growth of the field; and lastly, (3) point the literature take-home messages and conclusions, evidencing the main challenges and future opportunities that lie ahead, in particular for the development of novel machine learning (ML) algorithms in the context of emotion recognition using physiological signals.