A statistical associating fluid theory for potentials of variable range to model dipolar fluids is presented. The new theory, termed the SAFT-VR+D equation (the statistical associating fluid theory for potentials of variable range plus dipole), explicitly accounts for dipolar interactions and their effect on the structure of the fluid. This is achieved through the use of the generalized mean spherical approximation (GMSA) to describe a reference fluid of dipolar square-well segments. Isothermal-isobaric and Gibbs ensemble Monte Carlo simulations have been performed in order to test the new theoretical approach. Predictions for the thermodynamic properties and phase behavior of dipolar square-well monomer and chain fluids, in which one or more segments are dipolar, are considered and compared with new computer simulation data. The results show that the equation of state in general provides a good description of the phase behavior of dipolar monomer and chain fluids. Some deviations are seen between the simulation data and theoretical predictions for monomer fluids with large dipole moments and for molecules composed of segments with dipoles in different orientations. This is addressed through the replacement of the GMSA by the linearized exponential approximation.