Optical spectroscopy and scanning tunneling microscopy are used to study the size and shape dependence of the electronic states in CdSe quantum rods. Samples having average rod dimensions ranging from 10 to 60 nm in length and 3.5 to 7 nm in diameter, with aspect ratios varying between 3 to 12, were investigated. Both size-selective optical spectroscopy and tunneling spectra on single rods show that the level structure depends primarily on the rod diameter and not on length. With increasing diameter, the band gap and the excited state level spacings shift to the red. The level structure is assigned using a multi-band effective-mass model. We shall also discuss the effect of single electron charging on the tunneling spectra, possibly reflecting the quantum rod level degeneracy, and its dependence on the tunneling junction parameters.