Agent-based computational economics (ACE) has been used for tackling major research ques- tions in macroeconomics for at least two decades. This growing field positions itself as an alternative to dynamic stochastic general equilibrium (DSGE) models. In this paper, we pro- vide a much needed review and synthesis of this literature and recent attempts to incorporate insights from ACE into DSGE models. We first review the arguments raised against DSGE in the macroeconomic ACE (macro ACE) literature, and then review existing macro ACE models, their explanatory power and empirical performance. We then turn to the literature on behavioural New Keynesian models that attempts to synthesise these two approaches to macroeconomic modelling by incorpo...