The sophistication with which we can now prepare and characterize inorganic nanoparticles has inspired new areas of research into the fundamental properties and applications of these fascinating nanoscale systems. In this article some of the recent ideas concerning control of their optical properties are examined and explained, focusing on semiconductor nanocrystals. It is known that the optical properties of nanocrystals can be size-tunable, but it is less obvious how shape matters. To explain how size as well as shape matters, the electronic structure of nanocrystals is sketched in relatively simple terms, leading to an introduction to deeper concepts at the heart of spectroscopy such as the exciton fine structure. The exciton fine structure states, although obscured by inhomogeneous line broadening, dictate selection rules for optical excitation. These viewpoints are compared and contrasted to well-established principles in molecular spectroscopy that provide inspiration as well as perspective. The control of optical poperties is founded on our ability to prepare good quality colloidal particles. Recent advances in nanocrystal shape control are described. The current status of heterostructures is examined, with an emphasis on charge separation in CdSe–CdTe nanorods.