Vesicles, organelles and other intracellular cargo are transported by kinesin and dynein motors, which move in opposite directions along microtubules. This bidirectional cargo movement is frequently described as a 'tug of war' between oppositely directed molecular motors attached to the same cargo. However, although many experimental and modelling studies support the tug-of-war paradigm, numerous knockout and inhibition studies in various systems have found that inhibiting one motor leads to diminished motility in both directions, which is a 'paradox of co-dependence' that challenges the paradigm. In an effort to resolve this paradox, three classes of bidirectional transport models--microtubule tethering, mechanical activation and steric disinhibition--are proposed, and a general mathematical modelling framework for bidirectional cargo transport is put forward to guide future experiments.