The detection of extrasolar planets that transit periodically in front of their host stars has become a well-known technique over the past about 20 years with thousands of discoveries until today. The detection of moons transiting their stars together with their respective host planets, however, is much more challenging. This ongoing search has culminated in a staggering count of zero secure detections so far. Two exomoon candidates, giant super-Earth-sized moons around Kepler-1625b and Kepler-1708b, have recently been proposed in the literature. I will use these two cases to illustrate the software, data analysis, and statistical metrics involved in photodynamical modeling and to point out the challenges and obstacles in finding transits of extrasolar moons.