The integration of business process management (BPM) with artificial intelligence (AI) is driving unprecedented advancements in the creation of trustworthy, intelligent information systems. On the one hand, BPM poses unconventional, relevant questions about processes and the event data produced during their execution. On the other hand, AI offers established techniques that must be adapted and further enhanced to address these questions effectively. This synergy is particularly impactful in the case of flexible processes, which are best represented using a declarative approach – emphasising the temporal constraints that must be respected by the process, instead of explicitly detailing all the acceptable flows of activities. In this article, we overview how automated reasoning and learning techniques for temporal logics on finite traces provide robust foundations for representing, mining, and synthesising declarative processes. We cover established results as well as frontier research in this area.