In this article, we review eye-tracking studies with dogs (Canis familiaris) with a threefold goal; we highlight the achievements in the field of canine perception and cognition using eye tracking, then discuss the challenges that arise in the application of a technology that has been developed in human psychophysics, and finally propose new avenues in dog eye-tracking research. For the first goal, we present studies that investigated dogs' perception of humans, mainly faces, but also hands, gaze, emotions, communicative signals, goal-directed movements, and social interactions, as well as the perception of animations representing possible and impossible physical processes and animacy cues. We then discuss the present challenges of eye tracking with dogs, like doubtful picture-object equivalence, extensive training, small sample sizes, difficult calibration, and artificial stimuli and settings. We suggest possible improvements and solutions for these problems in order to achieve better stimulus and data quality. Finally, we propose the use of dynamic stimuli, pupillometry, arrival time analyses, mobile eye tracking, and combinations with behavioral and neuroimaging methods to further advance canine research and open up new scientific fields in this highly dynamic branch of comparative cognition.