Dogs have a remarkable skill to use human-given cues in object-choice tasks, but little is known to what extent their closest wild-living relative, the wolf can achieve this performance. In Study 1, we compared wolf and dog pups hand-reared individually and pet dogs of the same age in their readiness to form eye-contact with a human experimenter in an object-choice task and to follow her pointing gesture. The results showed that dogs already at 4 months of age use momentary distal pointing to find hidden food even without intensive early socialization. Wolf pups, on the contrary, do not attend to this subtle pointing. Accordingly in Studies 2 and 3, these wolves were tested longitudinally with this and four other (easier) human-given cues. This revealed that wolves socialized at a comparable level to dogs are able to use simple human-given cues spontaneously if the human's hand is close to the baited container (e.g. touching, proximal pointing). Study 4 showed that wolves can follow also momentary distal pointing similarly to dogs if they have received extensive formal training. Comparing the wolves to naïve pet dogs of the same age revealed that during several months of formal training wolves can reach the level of dogs in their success of following momentary distal pointing in parallel with improving their readiness to form eye-contact with a human experimenter. We assume that the high variability in the wolves' communicative behaviour might have provided a basis for selection during the course of domestication of the dog.