Rabies virus is a prototypical neurotropic virus that causes one of the most dangerous zoonotic diseases in humans. Humanized or fully human monoclonal antibodies (mAb) that neutralize rabies virus would be the basis for powerful post-exposure prophylaxis of rabies in humans, having several significant benefits in comparison with human or equine rabies polyclonal immunoglobulins. The most advanced antibodies should broadly neutralize natural rabies virus isolates, bind with conserved antigenic determinants of the rabies virus glycoprotein, and show high neutralizing potency in assays in vivo. The antibodies should recognize nonoverlapping epitopes if they are used in combination. This review focuses on basic requirements for anti-rabies therapeutic antibodies. The urgency in the search for novel rabies post-exposure prophylaxis and methods of development of anti-rabies human mAb cocktail are discussed. The rabies virus structure and pathways of its penetration into the nervous system are also briefly described.