Dogs' comprehension of human gestures has been characterized as more human-like than that of our closest primate relatives, due to a level of flexibility and spontaneous performance on par with that of human infants. However, many of the critical experiments that have been the core evidence for an understanding of human communicative intentions in dogs have yet to be replicated. Here we test the ability of dogs to comprehend a pointing gesture while varying the salience of the gesture and the context in which it is made. We find that subjects' (N = 70) choices across two experiments are consistent with an understanding of communicative intentions. Results largely replicate previous critical controls that rule out a number of egocentric hypotheses including an attraction to human hands and novelty. We also find that dogs spontaneously follow a human gesture in a new context: choosing which direction to navigate around a barrier. The flexible and spontaneous problem solving observed in dogs' gesture comprehension is discussed in relation to its similarity to that of human infants. We conclude with important avenues for future research.