Spatial heterogeneity (SH) is generally defined as the complexity and variability of a system property (e.g., plant biomass, cover) in space. Despite its importance in both theoretical and applied ecology, a formal and rigorous definition of SH is lacking. Such a definition is needed to facilitate quantitative analyses. To this end, we suggest that SH must be defined in terms of its underlying components. For categorical maps, SH is the complexity in five components: (1) number of patch types, (2) proportion of each type, (3) spatial arrangement of patches, (4) patch shape, and (5) contrast between neighboring patches. To illustrate the use of these components to develop a quantitative definition of SH, we used statistical models to produce categorical maps with known underlying SH characteristics. These simulated maps were analyzed in a factorial experiment to examine the effectiveness and sensitivity of four indices (i.e., fractal, contagion, evenness, patchiness) to detect patterns in these underlying components of SH. Our results show that any definition of SH is strongly dependent on the underlying variables and the methods used, that many indices depict different aspects of SH, that significant interactions exist among the five components of SH, and that some indices are strongly correlated. Quantification of spatial heterogeneity is essential to our understanding of the relationships between spatial heterogeneity and landscape functions and processes. However, all techniques to measure SH must be evaluated against systems with known characteristics of SH. Such a system is developed and used in this study.