A comparative study is made of the following bond orders: MO bond orders of Coulson, MO bond orders of Mulliken, MO bond populations of Platt-Ruedenberg-Scherr, VB bond orders of Pauling. The comparison is carried through on the basis of theoretical derivations and on the basis of numerical calculations for a large number of molecules. The main results are: an accurate functional connection between the Coulson and Mulliken bond orders; the characterization of a new type of bond order based on bond populations, and related linearly to bond lengths; a MO expression for VB bond orders.