Perturbation theory of effective Hamiltonians -- Folded diagram theory, time-dependent approach of Johnson and Baranger -- A time-dependent, diagrammatic analysis of effective interactions and operators -- Determination of effective matrix elements from experimental data -- How do we decide which unperturbed basis to use? What is the role of self-consistency? -- Computation of the reaction matrix, G -- Perturbation calculation in a double-partitioned Hilbert space -- The average effective interaction -- Algebraic structure of effective interactions and operators. Convergence properties of the perturbation expansions -- Is there a universal relationship connecting all two-body effective interactions? -- Relevant aspects of statistical spectroscopy -- Infinite partial summations -- Pade approximants and the calculation of effective interactions -- Shell model diagonalizations in an expanded space -- Density dependent interactions -- Calculation of other effective operators -- Theory versus theory as a test of the effective interaction -- Summary Talk: Where do we stand at the present time regarding the microscopic theory of effective interactions and operators?.