We describe the fundamentals of two new types of fiber, photonic crystal fiber (PCF) and photonic bandgap fiber (PBF). PCF is fabricated by forming small air holes in the cladding of the fiber rather than doping the fiber core with high-index materials. This fiber has very interesting new features including endlessly single-mode operation, zero GVD in the visible region, and an easily controllable spot-size due to the strongly guiding characteristics that result from the very high relative refractive index between the core and air-holed cladding. By contrast, PBF has air holes not only in its cladding but also in its core, and this enables us to confine an optical beam by using the principle of two-dimensional Bragg diffraction. The air core structure greatly reduces fiber nonlinearity and suggests the feasibility of high power transmission.