Given the detection of several thousand extrasolar planets, a very interesting question is whether or not they have moons or rings. In the cases of extrasolar Jupiter analogs, the gas giant may not support life, but a moon could be suitable. Exomoons or rings have not yet been detected with Kepler data, but the directly imaged Fomalhaut b is thought to be optically bright because of stellar light scattering off a circumplanetary dust ring (Kalas et al. 2008) and the distant (650 AU separation) 11 Jupiter mass planet HD 106906b has been possibly resolved in the optical using HST (Kalas et al. 2015). Also, the complex light curve of J1407 has been modeled as a circumplanetary ring system with radius 0.6 AU (Kenworthy & Mamajek 2015), and the 11 Jupiter mass planet FW Tau b displays accretion signatures (Bowler et al. 2014) as well as ALMA continuum emission from a circumplanetary disk (Kraus et al. 2014). In this talk I will review these results, and then describe international efforts to detect the possible moons and rings surrounding the massive planet Beta Pic b as its circumplanetary environment transits the star over a six-month period in 2017.