Eye tracking has been widely used for decades in vision research, language and usability. However, most prior research has focused on large desktop displays using specialized eye trackers that are expensive and cannot scale. Little is known about eye movement behavior on phones, despite their pervasiveness and large amount of time spent. We leverage machine learning to demonstrate accurate smartphone-based eye tracking without any additional hardware. We show that the accuracy of our method is comparable to state-of-the-art mobile eye trackers that are 100x more expensive. Using data from over 100 opted-in users, we replicate key findings from previous eye movement research on oculomotor tasks and saliency analyses during natural image viewing. In addition, we demonstrate the utility of smartphone-based gaze for detecting reading comprehension difficulty. Our results show the potential for scaling eye movement research by orders-of-magnitude to thousands of participants (with explicit consent), enabling advances in vision research, accessibility and healthcare.