On-chip optical isolators constitute an essential building block for photonic integrated circuits. Monolithic magnetooptical isolators on silicon, while featuring unique benefits such as scalable integration and processing, fully passive operation, large dynamic range, and simple device architecture, had been limited by their far inferior performances compared to their bulk counterparts. Here we discuss our recent work combining garnet material development and isolator device design innovation, which leads to a monolithic optical isolator with an unprecedented low insertion loss of 3 dB and an isolation ratio up to 40 dB. To further overcome the bandwidth and polarization limitations, we demonstrated broadband optical isolators capable of operating for both TM and TE modes. These results open up exciting opportunities for scalable integration of nonreciprocal optical devices with chip-scale photonic circuits.