Understanding how human trust in AI evolves over time is essential to identify the limits of each party and provide solutions for optimal collaboration. With this goal in mind, we examine the factors that directly or indirectly influence trust, whether they come from humans, AI, or the environment. We then propose a summary of methods for measuring trust, whether subjective or objective, to show which ones are best suited for longitudinal studies. We then focus on the main driving force behind the evolution of trust: feedback. We justify how learning feedback can be transposed to trust and what types of feedback can be applied to impact the evolution of trust over time. After understanding the factors that influence and how to measure trust, we propose an application example on a maritime surveillance tool with an AI-based decision aid.