Empirical studies have demonstrated that across changes in their sensory environment or input statistics, cortical neurons display a homeostasis or equalisation of firing rates. We present a normative explanation of such firing rate homeostasis grounded in efficient coding theory and the infomax principle. We further demonstrate how homeostatic coding, coupled with Bayesian theories of neural representation can explain stimulus-specific adaptation effects, which is widely observed in the nervous system (e.g., in the visual cortex), and how it can be achieved by divisive normalisation with adaptive weights.