This paper surveys the neoclassical theory of aggregate investment and its criticisms. We identify four main strands in neoclassical investment theory: (i) the traditional Wicksellian model; (ii) the Fisherian ‘array-of-opportunities’ approach; (iii) the Jorgensonian model; (iv) the now prevailing adjustment cost models. We summarize each approach, discuss the main conceptual issues, and highlight similarities and differences between them. We also provide a systematic summary and discussion of the main criticisms that have been leveled at each of these models and highlight some unresolved theoretical issues.