Silicon photonic integrated circuits comprising electro-optic modulators are key to a broad spectrum of applications. However, while the silicon photonics platform takes advantage of the well-established complementary metal-oxide-semiconductor (CMOS) processing technology for fabricating silicon-on-insulator (SOI) waveguides with high reproducibility, crystalline silicon lacks a second-order nonlinear susceptibility, which limits the functionality of the entire integration platform. The plasma dispersion effect provides an alternative means to change the refractive index by injection or depletion of carriers, but this approach has some disadvantages with respect to speed, efficiency, and footprint. Complementing silicon with Pockels-type organic electrooptic materials (silicon-organic hybrid, SOH) can overcome these limitations. In this review, we describe state-of-the-art organic electro-optic materials, address promising strategies to resolve stability concerns, discuss fabrication technologies, and we elaborate on the design of SOH Mach-Zehnder modulators (MZM). Our discussion on performance and applications of SOH MZM starts with the definition of metrics by which various modulator realizations can be compared. Beyond the standard use of SOH MZM, we draw attention to unconventional applications like optical readout of cryoelectronic circuits and other emerging areas in metrology and sensing which are so far not in the primary focus of the community.