Carbonyl, olefins, and phosphines are fundamental ligands in organometallic complex chemistry. Complexes containing these ligands are discussed in detail in this chapter. The bond between a transition metal (M) and a carbonyl ligand (CO) consists of both σ-donation and π-back-donation. The wavenumber of the stretching vibration of the CO bond (ν_CO) in the infrared absorption spectrum of a transition metal carbonyl complex is a very useful indicator of the strength of the M–CO bond. Estimation of the relative strength of the M–CO bond from the ν_CO value of carbonyl complexes is explained. The coordination of olefin ligands is similar to that of a carbonyl: the coordination consists of both σ-donation and π-back-donation. In the case of an olefin ligand, the relative contributions of σ-donation and π-back-donation depend on the oxidation state of the transition metal, the other ligands on the metal, the character of the olefin substituents and other factors, and are explained in this chapter. Phosphines (PR₃) are widely used in organometallic chemistry. By changing the kind of phosphine, the electronic state and steric environment of the central metal can be appropriately tuned. The relationship of the electron-donating property of R with the basicity of the phosphine ligand, and how this affects the electron density on the transition metal, are explained. Tolman's cone angle, used to estimate the steric effects of phosphine ligands, is also explained.