Integrated optical signal processors have been identified as a powerful engine for optical processing of microwave signals. They enable wideband and stable signal processing operations on miniaturized chips with ultimate control precision. As a promising application, such processors enables photonic implementations of reconfigurable radio frequency (RF) filters with wide design flexibility, large bandwidth, and high-frequency selectivity. This is a key technology for photonic-assisted RF front ends that opens a path to overcoming the bandwidth limitation of current digital electronics. Here, the recent progress of integrated optical signal processors for implementing such RF filters is reviewed. We highlight the use of a low-loss, high-index-contrast stoichiometric silicon nitride waveguide which promises to serve as a practical material platform for realizing high-performance optical signal processors and points toward photonic RF filters with digital signal processing (DSP)-level flexibility, hundreds-GHz bandwidth, MHz-band frequency selectivity, and full system integration on a chip scale.