Empathy, the capacity to recognize and share feelings experienced by another individual, is an important trait in humans, but is not the same as pro-sociality, the tendency to behave so as to benefit another individual. Given the importance of understanding empathy's evolutionary emergence, it is unsurprising that many studies attempt to find evidence for it in other species. To address the question of what should constitute evidence for empathy, we offer a critical comparison of two recent studies of rescuing behaviour that report similar phenomena but are interpreted very differently by their authors. In one of the studies, rescue behaviour in rats was interpreted as providing evidence for empathy, whereas in the other, rescue behaviour in ants was interpreted without reference to sharing of emotions. Evidence for empathy requires showing that actor individuals possess a representation of the receiver's emotional state and are driven by the psychological goal of improving its wellbeing. Proving psychological goal-directedness by current standards involves goal-devaluation and causal sensitivity protocols, which, in our view, have not been implemented in available publications. Empathy has profound significance not only for cognitive and behavioural sciences but also for philosophy and ethics and, in our view, remains unproven outside humans.