With its unique and exclusive linear and nonlinear optical characteristics, epsilon-near-zero (ENZ) photonics has drawn a tremendous amount of attention in the recent decade in the fields of nanophotonics, nonlinear optics, plasmonics, light-matter interactions, material science, applied optical science, etc. The extraordinary optical properties, relatively high tuning flexibility, and CMOS compatibility of ENZ materials make them popular and competitive candidates for nanophotonic devices and on-chip integration in all-optical and electro-optical platforms. With exclusive features and high performance, ENZ photonics can play a big role in optical communications and optical data processing. In this review, we give a focused discussion on recent advances of the theoretical and experimental studies on ENZ photonics, especially in the regime of nonlinear ENZ nanophotonics and its applications. First, we overview the basics of the ENZ concepts, mechanisms, and nonlinear ENZ nanophotonics. Then the new advancements in theoretical and experimental optical physics are reviewed. For nanophotonic applications, the recent decades saw rapid developments in various kinds of different ENZ-based devices and systems, which are discussed and analyzed in detail. Finally, we give our perspectives on where future endeavors can be made.