This work focuses on facial processing, which refers to artificial intelligence (AI) systems that take facial images or videos as input data and perform some AI-driven processing to obtain higher-level information (e.g. a person's identity, emotions, demographic attributes) or newly generated imagery (e.g. with modified facial attributes). Facial processing tasks, such as face detection, face identification, facial expression recognition or facial attribute manipulation, are generally studied as separate research fields and without considering a particular scenario, context of use or intended purpose. This paper studies the field of facial processing in a holistic manner. It establishes the landscape of key computational tasks, applications and industrial players in the field in order to identify the 60 most relevant applications adopted for real-world uses. These applications are analysed in the context of the new proposal of the European Commission for harmonised rules on AI (the AI Act) and the 7 requirements for Trustworthy AI defined by the European High Level Expert Group on AI. More particularly, we assess the risk level conveyed by each application according to the AI Act and reflect on current research, technical and societal challenges towards trustworthy facial processing systems.