The brain extracts behaviourally relevant sensory input to produce appropriate motor output. On the one hand, our constantly changing environment requires this transformation to be plastic. On the other hand, plasticity is thought to be balanced by mechanisms ensuring constancy of neuronal representations in order to achieve stable behavioural performance. Yet, prominent changes in synaptic strength and connectivity also occur during normal sensory experience, indicating a certain degree of constitutive plasticity. This raises the question of how stable neuronal representations are on the population level and also on the single neuron level. Here, we review recent data from longitudinal electrophysiological and optical recordings of single-cell activity that assess the long-term stability of neuronal stimulus selectivities under conditions of constant sensory experience, during learning, and after reversible modification of sensory input. The emerging picture is that neuronal representations are stabilized by behavioural relevance and that the degree of long-term tuning stability and perturbation resistance directly relates to the functional role of the respective neurons, cell types and circuits. Using a ‘toy’ model, we show that stable baseline representations and precise recovery from perturbations in visual cortex could arise from a ‘backbone’ of strong recurrent connectivity between similarly tuned cells together with a small number of ‘anchor’ neurons exempt from plastic changes.This article is part of the themed issue ‘Integrating Hebbian and homeostatic plasticity’.