This article presents a broad review on optical, radio-frequency (RF), microwave (MW), millimeter wave (mmW) and terahertz (THz) biosensors. Biomatter-wave interaction modalities are considered over a wide range of frequencies and applications such as detection of cancer biomarkers, biotin, neurotransmitters and heart rate are presented in detail. By treating biological tissue as a dielectric substance, having a unique dielectric signature, it can be characterized by frequency dependent parameters such as permittivity and conductivity. By observing the unique permittivity spectrum, cancerous cells can be distinguished from healthy ones or by measuring the changes in permittivity, concentration of medically relevant biomolecules such as glucose, neurotransmitters, vitamins and proteins, ailments and abnormalities can be detected. In case of optical biosensors, any change in permittivity is transduced to a change in optical properties such as photoluminescence, interference pattern, reflection intensity and reflection angle through techniques like quantum dots, interferometry, surface enhanced raman scattering or surface plasmon resonance. Conversely, in case of RF, MW, mmW and THz biosensors, capacitive sensing is most commonly employed where changes in permittivity are reflected as changes in capacitance, through components like interdigitated electrodes, resonators and microstrip structures. In this paper, interactions of EM waves with biomatter are considered, with an emphasis on a clear demarcation of various modalities, their underlying principles and applications.