We have successfully fabricated single-crystalline CdSe nanowires, nanobelts, and sheets by a chemical vapor deposition (CVD) method assisted with laser ablation. The synthesized CdSe nanostructures have hexagonal wurtzite phase as characterized by X-ray diffraction (XRD). CdSe nanobelts can range in length from several tens to a hundred micrometers, in thickness from 40 to 70 nm, and a tapered width which is similar to 3 mu m at one end and tapers off to similar to 100 nm at a catalytic gold particle. Both selected area electron diffraction (SAED) and high-resolution transmission electron microscopic (HRTEM) measurements show that the single-crystalline hexagonal belts and sheets grew along the [0 1 -1 0] direction with side surface of +/-(0 0 0 1) and top surface of +/-(2 -1 -1 0). While the growth mechanism of nanobelts complies with a combination of vapor-liquid-solid (VLS) and vapor-solid (VS) processes, the formation of sheets is primarily based on the VS mechanism. For comparison, the phonon modes of CdSe nanobelts and bulk powder have been measured by surface-enhanced Raman scattering (SERS) and normal Raman scattering (NRS) spectroscopies with off- and near-resonant excitations. A blue-shift of 2.4 cm(-1) for the longitudinal optical (LO) phonon of CdSe nanobelts, relative to bulk CdSe, is attributed to a lattice contraction in the belt structure, which is confirmed by the XRD measurement. Room-temperature microphotoluminescence (PL) at similar to 1.74 eV from single CdSe nanobelts shows a 3-fold enhancement compared to that from bulk CdSe powder and displays a partial polarization dependence of emission angles.