Delays are inherent to most dynamical systems. Besides shifting the process in time, they can significantly affect their performance. For this reason, it is usually valuable to study the delay and account for it. Because they are dynamical systems, it is of no surprise that sequential decision-making problems such as Markov decision processes (MDP) can also be affected by delays. These processes are the foundational framework of reinforcement learning (RL), a paradigm whose goal is to create artificial agents capable of learning to maximise their utility by interacting with their environment. RL has achieved strong, sometimes astonishing, empirical results, but delays are seldom explicitly accounted for. The understanding of the impact of delay on the MDP is limited. In this dissertation, we propose to study the delay in the agent's observation of the state of the environment or in the execution of the agent's actions. We will repeatedly change our point of view on the problem to reveal some of its structure and peculiarities. A wide spectrum of delays will be considered, and potential solutions will be presented. This dissertation also aims to draw links between celebrated frameworks of the RL literature and the one of delays.

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