Affective computing is an emerging interdisciplinary field where computational systems are developed to analyze, recognize, and influence the affective states of a human. It can generally be divided into two subproblems: affective recognition and affective generation. Affective recognition has been extensively reviewed multiple times in the past decade. Affective generation, however, lacks a critical review. Therefore, we propose to provide a comprehensive review of affective generation models, as models are most commonly leveraged to affect others' emotional states. Affective computing has gained momentum in various fields and applications, thanks to the leap of machine learning, especially deep learning since 2015. With critical models introduced, this work is believed to benefit future research on affective generation. We conclude this work with a brief discussion on existing challenges.