In extensively modified landscapes, how the matrix is managed determines many conservation outcomes. Recent publications revise popular conceptions of a homogeneous and static matrix, yet we still lack an adequate conceptual model of the matrix. Here, we identify three core effects that influence patch-dependent species, through impacts associated with movement and dispersal, resource availability, and the abiotic environment. These core effects are modified by five 'dimensions': spatial and temporal variation in matrix quality; spatial scale; temporal scale of matrix variation; and adaptation. The conceptual domain of the matrix, defined as three core effects and their interaction with these five dimensions, provides a much-needed framework to underpin management of fragmented landscapes and highlights new research priorities.