Light works great in an ordinary microscope, but the wavelength of visible light limits our ability to see small stuff. To 'see' small stuff, you need light with short wavelengths. Pretty soon you need x-rays and higher-energy photons (with shorter wavelengths). But x-rays are hard to focus and hard to measure precisely from where they come. So instead a favorite projectile is the electron.
Electron microscopes work by throwing energetic electrons at a target specimen and looking at how they bounce off. The higher the energy of the electrons, the shorter their quantum-mechanical wavelength, and the smaller the features can be resolved. Electron microscopes are very useful, but cannot see inside the nucleus of atoms unless the energy is very very high.