This paper presents an analysis of a class of latent heat storage systems (LHSS). The analysis is based on a lumped model (the basic model) that allows a broad class of LHSSs to be completely specified, with only two parameters and a set of operating temperatures, while still retaining the main thermodynamic aspects associated with its operation. Characterization of the performance in this manner permits the broad base application potential of such systems to be viewed. This modeling is in contrast to most studies to date, which employ many parameters to include details of specific systems, and therefore obscure, to a great extent, this broad-based application potential. The basic model is later modified in three ways to analyze operating conditions that either occur in practical units or are desirable for an improved operation of the units. The modifications include, first the consideration of the LHSS as being formed by many independent phase-change material (PCM) capsules. Second, the possibility of having PCMs with different phase change temperatures filling the capsules. Third, the case when the PCM melts over a temperature range. The results indicate that the efficiency of the basic model represents a higher bound for the efficient operation of LHSSs with negligible sensible storage capacity, and a single PCM. Using multiple PCMs within a LHSS results in higher efficiencies. These efficiencies set higher bounds for efficiency of any sensible or latent heat storage system, and also represent the only possibility for reversible operation of LHSS.