The thesis is divided into two parts．The first part is a survey on classical representability theorems．The emphasis is on the role of triangulated structure，i.e.　　 Krauses theorem and Franks theorem．Durlllg thediscussloll we made the observation that not only do the two theore have different proofs， but also they are of very different natures． In the second Part，we show that Frankes theorem（and itsproof) admits a direct generalization to unstable case,i.e.Kellers right rtiangulated categories.