This thesis investigates moral hazard problems and issues related to banks' risk-taking; it delivers implications with regard to prudential regulation, dynamic incentive contracts, and capital structure. In the first chapter, I develop a continuous-time model in which a principal hires an agent to run a risky project exposed to unpredictable events that may generate potentially large losses. Although event occurrences are beyond the control of the agent, the distribution of the random losses they generate is shaped by the agent's unobservable risk mitigation effort. I study optimal incentive contracts and show how these contracts strike a delicate balance between supporting and punishing the agent in the face of downside risk. In the second chapter, I adopt a dynamic contracting framework in order to study the design of incentive-based regulations of a bank engaging in a double moral hazard. In addition to shirking, the bank's manager can engage in risk-taking, which enhances short-term profits while increasing the bank's exposure to tail risk. Under the regulation optimising the bank's private value, excessive risk-taking and regulatory forbearance emerge when the bank is undercapitalised. The chapter then shows how the socially optimal regulator, which internalises the negative externalities of the bank's strategies on the economy, can guarantee the bank's continuation under a safe management. In the last chapter I propose an empirical study to assess the effects of monetary policy on banks' risk-taking. The study focuses on the impact of monetary shocks on banks' financial distress and lending during the recent financial crisis period characterised by money market rates near the lower bound and unconventional monetary measures. The analysis combines macroeconomic and bank-level data for a set of euro area banks using a factor-augmented autoregressive model. In line with the agency literature, a risk-taking channel arises for banks with low levels of capital.