Passive optical isolators are needed in silicon photonics but unavailable due to challenges in rare-earth iron garnet processing and integration. Material challenges include incompatibility with silicon and high annealing temperatures, and design challenges include a need for polarization diversity and a preference for no external magnetic bias. These challenges have restricted optical isolation to discrete modules that require physical pick and place of bulk garnet pieces. This review presents developments in the processing of magneto-optical garnets on Si and the enhancement of their Faraday rotation that enables small footprint isolators on silicon waveguide structures. For example, seedlayers and/or new garnet compositions have enabled monolithic Si integration, and in some cases, hybrid integration of garnet-on-garnet or transfer-printed garnet nanosheets enable reduced on-chip thermal processing. Integrated isolators that utilize non-reciprocal phase shift (NRPS) or non-reciprocal mode conversion (NRMC) have been demonstrated to have isolation ratios up to 30 dB, insertion loss as low as 9 dB, polarization diversity and magnet-free operation in the desired telecommunication wavelengths. The advances in materials, processing techniques, and isolator designs shown here will pave the way for on-chip isolators and novel multi-lane photonic architectures.