We propose a simple model to theoretically study the conductance of atomic-sized magnetic contacts. Our approach considers in detail the case of two-atom contacts with two spin channels, and the conductance is calculated using Landauer theory in the ballistic regime. For ferromagnetic contacts, we examine the large magnetoresistance effect obtained, when changing the magnetic configuration of the leads from parallel to antiparallel. We also discuss nonmagnetic transition metals nanocontacts, where conductance measurements display a behavior similar to magnetic contacts. Our treatment of the above phenomena reveals the important role played by quantum fluctuations in the contact region.726