A global health emergency resulted from the COVID-19 epidemic. Image recognition techniques are a useful tool for limiting the spread of the pandemic; indeed, the World Health Organization (WHO) recommends the use of face masks in public places as a form of protection against contagion. Hence, innovative systems and algorithms were deployed to rapidly screen a large number of people with faces covered by masks. In this article, we analyze the current state of research and future directions in algorithms and systems for masked-face recognition. First, the paper discusses the importance and applications of facial and face mask recognition, introducing the main approaches. Afterward, we review the recent facial recognition frameworks and systems based on Convolution Neural Networks, deep learning, machine learning, and MobilNet techniques. In detail, we analyze and critically discuss recent scientific works and systems which employ machine learning (ML) and deep learning tools for promptly recognizing masked faces. Also, Internet of Things (IoT)-based sensors, implementing ML and DL algorithms, were described to keep track of the number of persons donning face masks and notify the proper authorities. Afterward, the main challenges and open issues that should be solved in future studies and systems are discussed. Finally, comparative analysis and discussion are reported, providing useful insights for outlining the next generation of face recognition systems.