Gesture comprehension remains understudied, particularly in children with autism spectrum disorder (ASD) who have difficulties in gesture production. Using a novel gesture comprehension task, Study 1 examined how 2- to 4-year-old typically-developing (TD) children comprehend types of gestures and gesture-speech combinations, and showed better comprehension of deictic gestures and reinforcing gesture-speech combinations than iconic/conventional gestures and supplementary gesture-speech combinations at each age. Study 2 compared verbal children with ASD to TD children, comparable in receptive language ability, and showed similar patterns of comprehension in each group. Our results suggest that children comprehend deictic gestures and reinforcing gesture-speech combinations better than iconic/conventional gestures and supplementary combinations--a pattern that remains robust across different ages within TD children and children with ASD.