My dissertation investigates the nonlinear dynamics in business cycles and the transmission of monetary policy using both empirical and theoretical frameworks. Chapter 1 examines the impact of macroeconomic asymmetry on the welfare cost of business cycles. I investigate the welfare cost of business cycles due to asymmetries generated by two occasionally binding constraints (OBCs): downward nominal wage rigidity (DNWR) and zero lower bound (ZLB). Although business cycle volatility has declined recently as the Great Moderation literature suggests, I find that the welfare cost of business cycles has doubled due to the increased skewness of business cycles over time that is apparent in the data. In a quantitative dynamic equilibrium model that accounts for volatility and skewness changes in pre and postVolcker periods, I estimate that the welfare cost of business cycles has increased from 0.57% (in terms of consumption equivalence) in the pre-Volcker period to 0.97% in the post-Volcker period. Counterfactual analysis shows that while both OBCs play a role, the binding ZLB explains most of the welfare effects in the post-Volcker period. Policy counterfactuals indicate that increasing the inflation target from 2% to 4% reduces the skewness of business cycles and the binding rates of both OBCs, thereby leading to a significant decrease in the welfare cost, from 0.97% to 0.67%. In Chapter 2, I investigate the welfare maximizing steady-state inflation rate in a heterogeneousagent New Keynesian model with Downward Nominal Wage Rigidity (DNWR). After matching the annual wage change distribution in the U.S., I show that DNWR has a very significant impact on the economy when the inflation target is low. Considering the effect of the zero lower bound, price dispersion due to sticky prices, declining natural rate of interest, and lower trend productivity, I find that the optimal inflation target should be much higher than 2%, close to 7%. This result holds taking transition dynamics into account and is robust to a wide range of parameterizations. Lastly, Chapter 3 analyzes the impact of heterogeneity in wage and price stickiness on the transmission of monetary policy. Using the price and wage rigidity estimates of previous studies, I find a slightly negative correlation between wage and price rigidity at the industry level. After categorizing 3-digit industries as rigid and flexible, I analyze the impulse responses of real variables to a monetary policy shock. I document a significant response of industrial production in price-rigid industries, whereas in wage-rigid industries the response is still significant but weaker. Consistent with the theory, the response in price- and wage-flexible industries is not significant. The empirical results suggest that due to relatively lower variation in wage stickiness at the industry level, price stickiness plays a more important role in the differential response of industries to a monetary policy shock. Besides, I develop a multi-sector model incorporating sector-level heterogeneity both in wage and price rigidity into an otherwise standard New Keynesian model and analyze the monetary non-neutrality for different specifications. The results of the model verify the empirical findings.