Abstarct: A subset S of vertices in a graph G=(V,E) is a dominating set of G if every vertex in V-S has at least a neighbor in S. A dominating set S is a locating-dominating set of G if every two vertices x,y∈ V(G)-S satisfy N(x)∩ S≠ N(y)∩ S. The locating-domination number γ_L (G) is the minimum cardinality of a locating-dominating set of G. A subset S of vertices in a graph G is an identifying code if for every two vertices x and y of G, the sets N[x]∩S and N[y]∩S are non-empty and different. The minimum cardinality of an identifying code in G is denoted by M(G). In this thesis, we study the identifying and locating dominating codes and parameters dependent on these codes of graphs, and state some features, applications and bounds available for those parameters. Then, we improve some of these bounds and present new bounds for trees. Also, we characterize all trees achieving equality for the new bounds. Finally, we extend the Roman dominating function to locating Roman dominating function, and introduce a new parameter called the locating Roman domination number for graphs and study several bounds for this parameter on graphs and trees. Moreover, we compare this parameter with other graph parameters.