We study theoretically an active colloid whose polar axis of self-propulsion rotates to point parallel (antiparallel) to an imposed chemical gradient. We show that the coupling of this `chemotactic' (‘antichemotactic’) response to phoretic translational motion yields remarkable two-particle dynamics reflecting the non-central and non-reciprocal character of the interaction. A pair of mutually chemotactic colloids trap each other in a final state of fixed separation resulting in a selfpropelled active dieter. A second type of bound state is observed when the polar axes undergo periodic cycles leading to phase-locked circular motion around a common centre. A pair of swimmers with mismatched phoretic mobilities execute a dance in which they twirl around one another while moving jointly in a wide circle. For sufficiently small initial separation, the speed of self-propulsion controls the transition from bound to scattering states. Mutually anti-chemotactic swimmers always scatter apart. For the special case in which one of the two colloids has uniform surface activity we succeed in exactly classifying the fixed points underlying the bound states, and identify the bifurcations leading to transitions from one type of bound state to another. The varied dynamical behaviours are accessible by tuning the swimmer design and are summarised in state diagrams.