Digital holography with diffractive phase apertures is a hologram recording technique in which at least one of the interfering waves is modulated by a phase mask. In this review, we survey several main milestones on digital holography with dynamic diffractive phase apertures. We begin with Fresnel incoherent correlation holography (FINCH), a hologram recorder with an aperture of a diffractive lens. FINCH has been used for many applications such as 3D imaging, fluorescence microscopy, superresolution, image processing, and imaging with sectioning ability. FINCH has played an important role by inspiring other digital holography systems based on diffractive phase aperture, such as Fourier incoherent single-channel holography and coded aperture correlation holography, which also are described in this review.