This thesis investigates topics in macroeconomics with nonlinear dynamics as their inherent feature. It aims to further the understanding of the connection between the financial sector and economic fluctuations, challenges of monetary policy in a low interest rate environment and how to mitigate the macroeconomic consequences of a pandemic. The first chapter investigates the connection between the shadow banking sector and the vulnerability of the economy to a financial crisis. Motivated by the build-up of shadow bank leverage prior to the Great Recession, I develop a nonlinear macroeconomic model that features excessive leverage accumulation and show how this can cause a run. Introducing risk-shifting incentives to account for fluctuations in shadow bank leverage, I use the model to illustrate that extensive leverage makes the shadow banking system runnable, thereby raising the vulnerability of the economy to future financial crises. The model is taken to U.S. data with the objective of estimating the probability of a run in the years preceding the financial crisis of 2007-2008. The second chapter, joint with Francesco Bianchi and Leonardo Melosi, is motivated by the observation that the Federal Reserve Bank has been systematically undershooting its 2% inflation target in the past twenty years. This deflationary bias is a predictable consequence of the current symmetric monetary policy strategy that fails to recognize the risk of encountering the zero-lower-bound. An asymmetric rule according to which the central bank responds less aggressively to above-target inflation corrects the bias, improves welfare, and reduces the risk of deflationary spirals. The third chapter, joint with Matthieu Darracq Paries and Christoffer Kok, analyses the risk that an intended monetary policy accommodation might actually have contractionary effects in a low interest rate environment. We demonstrate that the risk of hitting the rate at which the effect reverses depends on the capitalization of the banking sector by using a nonlinear macroeconomic model. The framework suggests that the reversal interest rate is around −1% p.a. in the Euro Area. We show that the possibility of the reversal interest rate creates a novel motive for macroprudential policy. The fourth chapter, joint with Leonardo Melosi, studies contact tracing in a new macro-epidemiological model with asymptomatic spreaders. Contact tracing is a testing strategy that aims to reconstruct the infection chain of newly symptomatic agents. We show that contact tracing may be insufficient to stem the spread of infections because agents fail to internalize that their decisions increase the number of traceable contacts to be tested in the future. We provide theoretical underpinnings to the risk of becoming infected in macro-epidemiological models.