Automatic machine-based Facial Expression Analysis (FEA) has made substantial progress in the past few decades driven by its importance for applications in psychology, security, health, entertainment, and human- computer interaction. The vast majority of completed FEA studies are based on nonoccluded faces collected in a controlled laboratory environment. Automatic expression recognition tolerant to partial occlusion remains less understood, particularly in real-world scenarios. In recent years, efforts investigating techniques to handle partial occlusion for FEA have seen an increase. The context is right for a comprehensive perspective of these developments and the state of the art from this perspective. This survey provides such a comprehensive review of recent advances in dataset creation, algorithm development, and investigations of the effects of occlusion critical for robust performance in FEA systems. It outlines existing challenges in overcoming partial occlusion and discusses possible opportunities in advancing the technology. To the best of our knowledge, it is the first FEA survey dedicated to occlusion and aimed at promoting better-informed and benchmarked future work.