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This work aims to explore several research directions in stochastic sequential decision-making. The stochastic multi-armed bandit is a theoretical framework in which an agent must repeatedly decide among a predefined set of possible actions while receiving sequential feedback. The main challenge is balancing exploiting the most promising actions with exploring the whole set. An underlying mathematical model links different arms' rewards in bandits with structure. In real-world applications and theory, correctly exploiting this structure can remarkably boost an agent's performance. The focus of this work will be on bandits with temporal structure (i.e., time-dependent dynamics in the reward functions, such as the autoregressive bandits framework) and bandits with side-information feedback (i.e., settings in which the feedback is halfway between the full-information feedback and the bandit feedback, such as graph feedback or Lipschitz reward functions). The goal is to explore these settings and provide novel algorithms, together with theoretical results aimed at bridging the gap between different types of structures, presenting a unifying framework to analyze the theoretical guarantees of the provided approaches.