The problems of determining the minimum-size identifying, locating-dominating and open locating-dominating codes of an input graph are special search problems that are challenging from both the theoretical and computational viewpoints. In these problems, one selects a dominating set C from the vertex set V(G) of a graph G such that the vertices of a chosen subset of V(G) (i.e. either V(G)\ C or V(G) itself) are uniquely determined by their neighborhoods in C. A typical line of attack for these problems is to determine tight bounds for the minimum codes in various graphs classes. In this work, we present tight lower and upper bounds for all three types of codes for block graphs (i.e. diamond-free chordal graphs). Our bounds are in terms of the number of maximal cliques (or blocks) of the block graph and the order of the graph. Two of our upper bounds verify conjectures from the literature — with one of them being now proven for block graphs in this article. As for the lower bounds, we prove them to be linear in terms of both the number of blocks and the order of the block graph. For each of our bounds, we provide examples of families of block graphs whose minimum codes attain these bounds, thus showing each bound to be tight.