Optical imaging has been well-known in nature and in technology for decades. Recently, new methods of optical imaging assisted by techniques of computational imaging have been proposed and demonstrated. In the presentation, we describe several new techniques of three-dimensional optical imaging, from Fresnel Incoherent Correlation Holography (FINCH) to interferenceless Coded Aperture Correlation Holography (COACH). These systems have different imaging performances than conventional techniques. FINCH and COACH are methods for recording digital holograms of a three-dimensional scene. However, COACH can be used for several other incoherent and coherent optical applications. In this talk, we survey the prime landmarks on the topics of FINCH and COACH from two major perspectives: architectures and applications of the various systems. We explore the main configurations of hologram recorders in FINCH and COACH systems. For each design, we describe some of the recent implementations of these recorders in optical imaging. Possible applications for these imaging methods, ranging from a new generation of fluorescent microscopes to methods of noninvasive imaging through a scattering medium, will be discussed