It is well known that central bank policies affect not only macroeconomic aggregates, but also their distribution across economic agents. Similarly, a number of papers demonstrated that heterogeneity of agents may matter for the transmission of monetary policy to macro variables. Despite this, the mainstream monetary economics literature has so far been dominated by dynamic stochastic general equilibrium models with representative agents. This paper aims to tilt this imbalance towards heterogeneous agents setups by surveying the main positive and normative findings of this line of the literature, and suggesting areas in which these models could be implemented. In particular, we review studies that analyse the heterogeneity of (i) households’ income, (ii) households’ preferences, (iii) consumers’ age, (iv) expectations and (v) firms’ productivity and financial position. We highlight the results on issues that, by construction, cannot be investigated in a representative agent framework and discuss important papers modifying the findings from the representative agent literature.