We analyze the role of household heterogeneity for the response of the macroeconomy to aggregate shocks. After summarizing how macroeconomists have incorporated household heterogeneity and market incompleteness in the study of economic fluctuations so far, we outline an emerging framework that combines Heterogeneous Agents (HA) with nominal rigidities, as in New Keynesian (NK) models, that is much better aligned with the micro evidence on consumption behavior than its Representative Agent (RA) counterpart. By simulating consistently calibrated versions of HANK and RANK models, we convey two broad messages. First, the degree of equivalence between models crucially depends on the shock being analyzed. Second, certain interesting macroeconomic questions concerning economic fluctuations can only be addressed within HA models, and thus the addition of heterogeneity broadens the range of problems that can be studied by economists. We conclude by recognizing that the development of HANK models is still in its infancy and by indicating promising directions for future work.