Magnonic crystals can be regarded as the magnetic counterpart of photonic crystals, with spin waves acting as information carriers. Thus, magnonic crystals are magnetic materials with periodic distribution of the constituents or periodic modulation of some magnetic parameters (e.g., saturation magnetization or magnetocrystalline anisotropy), or other parameters relevant to the propagation of spin waves (e.g., external magnetic field, film thickness, stress, or a surrounding of the homogeneous ferromagnetic film). The spin waves propagating in magnonic crystal have a form of Bloch waves, and the dispersion relation includes frequency bands allowing spin wave propagation and frequency band gaps, forbidden for spin wave propagation. By adjusting relevant parameters of the magnonic crystal or external fields, the spectrum of spin waves can be tuned and the flow of spin waves can be tailored in the way unavailable with homogeneous media. The new physical effects occurring in magnetic nanostructures with periodic pattern and prospective applications of magnonic crystals, especially in integrated microwave devices and for processing information at microwave frequencies, drive the new fields of magnonics and magnon spintronics.