Responsive core–shell nanogels that consist of polymers with different sensitivities to an environmental stimulus are soft matter systems with very unique properties. The coupling of the networks leads to a mutual influence of swelling and thus affects the internal structure and dynamics. We highlight the recent progress in theoretical modelling that provides important information on the inhomogeneous internal structures of core–shell nanogels and also discuss interesting discrepancies between theoretical models and experimental data. In addition we describe amphoteric core–shell nanogels that reveal further specific properties, which are of utmost relevance for applications but very challenging for theoretical models. Finally we discuss unexpected dynamic properties of core–shell nanogels with shell-restricted swelling, which indicate confinement effects.