The miniaturization of optical systems has been a longstanding interest for physicists. By facilitating the design of smaller optical systems, we can improve their versatility and cost-effectiveness. This aim applies to macroscopic imaging systems, technologies that implicitly image, and micrometer-scale optics. Parallel to this, quantum optical devices have also seen rapid developments. Notably, the need for new quantum communications and quantum imaging devices has recently risen. The thesis outlines advancements in both of these areas and, in many ways, bridges gaps between them. It discusses the development of optics that compress free space, the design of holographic optical elements, and the generation of entangled photon states in thin-film sources. First, we describe an optic designed to miniaturize free space, termed the spaceplate. Spaceplates achieve the propagation of light for a distance greater than their thickness.Therefore, they compress optical space, reducing the required distance between optical elements in an imaging system. In this thesis, we describe a spaceplate based on conventional optics in a 4-f arrangement, mimicking the transfer function of free space in a thinner system - we term this device a three-lens spaceplate. It is broadband, polarization-independent, and achieves meter-scale space compression. We experimentally measure compression ratios up to 15.6, replacing up to 4.4 meters of free space, three orders of magnitude greater than previous spaceplates. We demonstrate that three-lens spaceplates reduce the length of a full-color imaging system, albeit with reductions in resolution and contrast. We also present theoretical limits on the numerical aperture and the compression ratio. Our design presents a simple, accessible, cost-effective method for optically compressing large volumes of space. Second, we discuss the design of holographic optical elements. Holograms are extraordinarily versatile optics. They have many applications, including interferometry, spectrometry, data storage, optical filtration, and sensing. We can design various optical elements such as filters, lenses, beam splitters, and solar concentrators by tailoring the phase response of a hologram. In this thesis, we describe the nature and function of holograms, and we experimentally characterize holography in lithium niobate and photopolymers. Using this characterization, we assess the limitations of different holographic analysis methods. Further, we describe novel holographic optical elements like the holographic spaceplate - a holographic optic element whose phase response mimics free space. Lastly, this thesis outlines the production of entangled photon pairs, or biphotons, via non-phase-matched spontaneous parametric down-conversion in micrometer- and nanometer-scale devices. By producing biphotons in micrometer-scale crystals rather than in bulk, as is done traditionally, we are allowed to ignore phase matching. These devices produce broadband emission in both angle and frequency not seen in phase-matched bulk sources. We measure entangled biphotons produced via spontaneous parametric down-conversion in gallium arsenide (111) and lithium niobate - both undoped and iron-doped. Lastly, we outline and present initial experiments towards a holographic spontaneous parametric down-conversion optic that combines photon production and mode sorting - an optic of cascaded miniaturization.