The recently observed acceleration of the expansion of the universe is a topic of intense interest. The favoured causes are the "cosmological constant" or "dark energy". The former, which appears in the Einstein equations as the term [lambda]g[subscript [mu]v], provides an extremely simple, well-defined mechanism for the acceleration. However, there is a school of thought that suggests that the cosmological constant is inadequate to explain fully the evolution of the universe and should be replaced by a slowly varying scalar field--the aforementioned dark energy. The situation is complicated by the circumstance that the expression for the cosmological constant is precisely that of the zero-point energy of a quantum field, [epsilon][subscript 0]g[subscript [mu]v]. This strongly suggests the two are related. There are several problems here. The "calculated" value of the various contributions to [epsilon][subscript 0] may be as much as 120 orders of magnitude greater than the "observed" value of [lambda]. How these contributions add up to so minute a quantity is a major part of what is commonly termed "the cosmological constant problem". Traces of dark energy have yet to be found. We review some of the history and problems associated with the concepts of the cosmological constant and dark energy, provide a brief review of the relevant cosmology and review possible candidates for dark energy. (Contains 17 footnotes.)