Synthetic microwave focusing methods have been widely adopted in qualitative medical imaging to detect and localize anomalies based on their electromagnetic scattering signatures. This paper discusses the principles, challenges, and limitations of synthetic microwave-focusing techniques in medical applications. It is shown that the various focusing techniques, including time reversal, confocal imaging, and delay-and-sum, are all based on the scalar solution of the electromagnetic scattering problem, assuming the imaged object, i.e., the tissue or object, is linear, reciprocal, and time-invariant. They all aim to generate a qualitative image, revealing any strong scatterer within the imaged domain. The differences among these techniques lie only in the assumptions made to derive the solution and create an image of the relevant tissue or object. To get a fast solution using limited computational resources, those methods assume the tissue is homogeneous and non-dispersive, and thus, a simplified far-field Green's function is used. Some focusing methods compensate for dispersive effects and attenuation in lossy tissues. Other approaches replace the simplified Green's function with more representative functions. While these focusing techniques offer benefits like speed and low computational requirements, they face significant ongoing challenges in real-life applications due to their oversimplified linear solutions to the complex problem of non-linear medical microwave imaging. This paper discusses these challenges and potential solutions.