Filaments are truly ubiquitous in the molecular cloud. Dense molecular filaments will fragment into gravitationally bound cores, most of which will evolve into stars. Continuous accretion of gas, geometrical bending, and magnetic fields may control the detailed fragmentation manner of the filaments. In supercritical filaments, observations have revealed quasi-periodic chains of dense cores with spacing of 0.15 parsec comparable to the filament inner width. A substantial fraction of filaments contained prestellar and protostellar cores, supporting the important role of filaments in gravitationally bound core formation. Recent studies have suggested that filamentary structures in molecular clouds play a crucial role in the initial conditions of star formation and the origin of the stellar IMF.