Optimality plays a central role in the area of statistical experimental design. In general, problems in design optimality are composed of two vital components. One of these is determining conditions under which a design is optimal (such as values of design parameter or special structure in the information matrix). The other is construction of designs satisfying those conditions. In block designs, optimality criteria are functions of the information matrix of designs. In this thesis, the A-optimality problem is pursued for three treatments in block designs and row-column layout. Depending on the number of rows and columns of the row-column design, the requirements for optimality can decidedly counterintuitive: replication numbers not be as equal as possible, and trace of the information matrix need not be maximal. General rules for comparing information matrices for their A-behavior are also developed. In chapter four of this thesis, E-optimality is studied for three treatments in an arbitrary n-way heterogeneity setting. In the last chapter, construction of A- and E-optimal block designs with three treatments are introduced.