In the exploration of quantum materials' electronic properties, microwave techniques uniquely enable probing the electromagnetic response, which reveals signatures of many exotic matter phases. Over the past decade, the advent of scanning microwave probes, notably Microwave Impedance Microscopy (MIM), has facilitated spatially resolved measurements, which can serve as a nearly disorder-free local probe of electromagnetic response. We recently proposed a theoretical MIM response framework grounded in linear response theory, allowing a more quantitative interpretation of the MIM signal and a more accurate analysis for 1D edge modes. In this talk, I will first outline this framework, then apply it to study (fractional) quantum anomalous Hall insulators, with Cr-doped Bi2Te3 and twisted MoTe2 as two examples. This approach not only demystifies several experimental observations but also identifies unique experimental signatures distinguishing topological edge modes from trivial ones. Further, I will demonstrate how MIM's frequency and momentum resolution can be leveraged to investigate composite Fermi liquid and pseudo-gap phases. Time permitting, I'll discuss related research on axion dynamics in axion insulators via microwave techniques.