The emergence of COVID-19 has had a global and profound impact, not only on society as a whole, but also on the lives of individuals. Various prevention measures were introduced around the world to limit the transmission of the disease, including face masks, mandates for social distancing and regular disinfection in public spaces, and the use of screening applications. These developments also triggered the need for novel and improved computer vision techniques capable of (i) providing support to the prevention measures through an automated analysis of visual data, on the one hand, and (ii) facilitating normal operation of existing vision-based services, such as biometric authentication schemes, on the other. Especially important here, are computer vision techniques that focus on the analysis of people and faces in visual data and have been affected the most by the partial occlusions introduced by the mandates for facial masks. Such computer vision based human analysis techniques include face and face-mask detection approaches, face recognition techniques, crowd counting solutions, age and expression estimation procedures, models for detecting face-hand interactions and many others, and have seen considerable attention over recent years. The goal of this survey is to provide an introduction to the problems induced by COVID-19 into such research and to present a comprehensive review of the work done in the computer vision based human analysis field. Particular attention is paid to the impact of facial masks on the performance of various methods and recent solutions to mitigate this problem. Additionally, a detailed review of existing datasets useful for the development and evaluation of methods for COVID-19 related applications is also provided. Finally, to help advance the field further, a discussion on the main open challenges and future research direction is given.