Though much is known about the emergence and development of gaze following in infancy, there are large disagreements in some critical areas and major uncertainties within others. In this work, we highlight some of these areas in terms of five big questions that we believe are essential to address in order to advance research in the field. (1) How does social environment and culture impact gaze following? (2) What mechanisms drive the emergence of gaze following? (3) Does gaze following facilitate language development? (4) Is diminished gaze following an early marker of Autism? (5) How does gaze following relate to perspective-taking? This chapter aims not to answer these questions but to stimulate a discussion about the fundamental principles and assumptions on which the field resides and potentially serve as a guide for future research programs.