A main challenge for modern macroeconomics is to understand the consequences of the sizeable heterogeneity across households and firms, a feature ignored by textbook representative-agent models. Important questions arise on the role that such heterogeneity plays in the workings of the economy and its ability to respond to shocks in the presence of frictions and lumpy behavior (infrequent large adjustments), as is the case for durable purchases, technology adoption, portfolio adjustments, investment and price re-setting. We develop new methods to characterize the equilibrium dynamics of rich distributions, for a rigorous understanding of the forces that impinge on the aggregate economic behavior in the presence of realistic heterogeneity. We apply the methods to two set of macroeconomic problems. First, mapping models to data and the economy’s response to shocks. For a broad class of models with lumpy behavior we analyze aggregation and develop methods to identify and quantify the fundamental frictions the agents face. The methods will be used to characterize the economy's response to aggregate shocks and identify the cross section features that matter (and those that do not) in shaping the aggregate response. Applications concern investment, labor and housing markets, inequality and growth, and new-keynesian models. Second, a rigorous analysis of dynamic strategic complementarities and network effects. The dependence of one agent's decision on what other agents do is key in modelling aggregate dynamics and relevant in reality. For instance, a firm may be slow to react to a shock because other firms have not yet reacted. To date there are no results to guide us in the analysis of such complementarities in dynamic models with heterogeneity. Several applications, including the amplification of monetary nonneutrality, and the dynamic network effects of introducing e.g. central bank digital currency, will be explored.