Coherence is a familiar concept in physics. It is the driving force behind wavelike phenomena such as the diffraction of light. Moreover, wave-particle duality implies that all quantum objects can exhibit coherence, and this quantum coherence is crucial to understanding the behaviour of a plethora of systems. In this paper, which is written at an undergraduate level, we shall briefly introduce what is meant by coherence in a well-known classical setting, before going on to describe its quantum version. We will show that coherence is important in describing the properties of solid-state nanosystems and especially quantum dots. Simple experiments that reveal the coherent nature of matter-and how this leads to some very powerful applications-will be described. Finally, we shall discuss the fragility of coherence and shall introduce a method for describing decoherence in open quantum systems.