The design, fabrication, and measurement of photonic-band-gap (PBG) waveguides and resonators in two-dimensional photonic crystal slabs have been investigated. Although photonic crystal slabs have only partial gaps, efficient waveguides and resonators can be realized by appropriate design. As regards PBG waveguides, we show various designs for efficient single-mode waveguides in PhC slabs with SiO2 cladding, we report group dispersion measurements of PBG waveguides in PhC slabs, and describe the successful fabrication of PBG waveguides with adiabatic connectors that enable us to couple the light from single-mode fibers efficiently to PBG waveguides. As regards PBG resonators, we show how to realize very high-Q and small volume resonators in hexagonal PhC slabs, and report the fabrication of resonant tunneling filters that consist of PBG resonators coupled with PBG waveguides. We also describe the successful fabrication of resonant tunneling mode-gap filters with adiabatic mode connectors.