Photonic-assisted receivers for instantaneous microwave frequency measurement are devices used to measure the instantaneous frequency and amplitude of one or more microwave signals in the optical range, typically used in radar systems. Increasingly higher demands are placed on frequency range, accuracy and resolution during the development of instantaneous microwave frequency measurement applications, and these demands can be satisfied by the creation of new devices and operating principles. To permit further development in this area, it is necessary to generalize the experience gained during the development of devices based on frequency and amplitude discriminators of resonance type, including advanced ones with the best performances. Thus, in this report, we provide an overview of all the basic types of approaches used for the realization of photonic-assisted receivers based on fiber Bragg gratings, integrated Fano and optical ring resonators, Brillouin gain spectrum, and so on. The principles of their operation, as well as their associated advantages, disadvantages, and existing solutions to identified problems, are examined in detail. The presented approaches could be of value and interest to those working in the field of microwave photonics and radar systems, as we propose an original method for choosing photonic-assisted receivers appropriate for the characterization of multiple frequency measurements.