Stability methods, as they are applied in describing the initiation, growth and long term evolution of morphological features, are discussed. In particular, their use in describing large-scale, long-term rhythmic morphological features is highlighted. The analysis of such models indicates that many rhythmic bottom features arise from an inherent instability of a morphodynamical system, rather than being forced by external conditions. A synopsis of their theoretical basis is given, and the assumptions commonly pertaining to their use are described. These models, which can be applied more efficiently than many other process-oriented models, are categorized, and the kind of information that they can provide is also described. Finally, their relation to other areas and techniques of long-term, aggregated scale morphodynamics is discussed, and their usefulness to and applicability by the practitioner is summarized.