Low-loss nano- and micro-photonic platforms provide strong optical confinement and as a result enhance the effective material nonlinearity by several orders of magnitude, making them appealing candidates for quantum nonlinear photonics. One such platform is based on high-Q crystalline whispering-gallery-mode (WGM) microresonators, which can provide for highly efficient three-wave mixing, where even a single photon has a strong effect. We present experimental progress on the fabrication of small microresonators (R≲100 μm) with Q-factors ≥ 10 6 that are capable of supporting such strong coupling. We also demonstrate direct imaging of the spatial profiles of the WGMs, which is useful for identifying the phase-matched resonances of three-wave-mixing processes. Additionally, we present theoretical modeling of the cavity dynamics which suggests that single-photon-driven nonlinear processes are feasible in these crystalline microresonators. This crystalline WGM microresonator platform, therefore, can enable deterministic generation of non-classical light, including entangling gates for quantum information processing.