Nervous systems use excitatory cell assemblies to encode and represent sensory percepts. Similarly, synaptically connected cell assemblies or "engrams" are thought to represent memories of past experience. Multiple lines of recent evidence indicate that brain systems create and use inhibitory replicas of excitatory representations for important cognitive functions. Such matched "inhibitory engrams" can form through homeostatic potentiation of inhibition onto postsynaptic cells that show increased levels of excitation. Inhibitory engrams can reduce behavioral responses to familiar stimuli, thereby resulting in behavioral habituation. In addition, by preventing inappropriate activation of excitatory memory engrams, inhibitory engrams can make memories quiescent, stored in a latent form that is available for context-relevant activation. In neural networks with balanced excitatory and inhibitory engrams, the release of innate responses and recall of associative memories can occur through focused disinhibition. Understanding mechanisms that regulate the formation and expression of inhibitory engrams in vivo may help not only to explain key features of cognition but also to provide insight into transdiagnostic traits associated with psychiatric conditions such as autism, schizophrenia, and posttraumatic stress disorder.