Until a few years ago, most transient transport studies observed primarily diffusive plasma transport responses to fast, localized perturbations. Recently, several experiments have, in addition, observed `non-local' electron heat responses. Most remarkably, in `cold-pulse' experiments the abrupt edge cooling via radiative processes can induce both a diffusive cooling response moving in from the edge and, simultaneously, a rising electron temperature in the central core of tokamak plasmas - an opposite response even before the diffusive cooling from the edge reaches the centre! These and other non-local electron heat transport conundra from recent experiments are reviewed. The models and physical processes advanced to explain these puzzling phenomena are also discussed. The importance of resolving this transport enigma is emphasized.