The blue phases are fascinating structures in liquid crystals, fluids that exhibit cubic structures that have true crystalline order. The blue phases were discovered in the 1970s and were the subject of extensive research in the 1980s, when a deep understanding of many of their properties was established. The discovery that the blue phases could be stabilised to exist over wide temperature ranges meant that they became more than scientific curiosities and led to a recent resurgence in research into them as they offer some promise in applications. This paper considers some important aspects of the blue phases that are recurrent topics in their research. It describes factors affecting blue phase stability, demonstrating on the role of the bend elastic constant; field effects, including the Kerr effect, electrostriction and relaxation phenomena; and alignment, in particular production and control of blue phase monodomains. The dependence of these phenomena on the physical properties of the liquid crystalline system, including the twist and bend elastic constants and the dielectric anisotropy, is emphasised wherever possible. The paper links work carried out in the 1980s with contemporary research, using a few key examples to show how there is still much to understand in this beautiful topic.