Order-disorder in alloys, oxides, and silicates is studied by means of Monte Carlo methods. The key objective is to take explicit account of atom relaxation and cluster formation without resorting to the use of a parametrized Hamiltonian. We use a variety of Monte Carlo techniques, ranging from an Ising model to a hybrid Monte Carlo/molecular dynamics scheme. It is crucial to lake account of relaxation of the local atomic environment and vibrational effects. We have investigated both convergent and nonconvergent ordering. Applications include (i) Cu/Au ordering in Cu-Au alloys, (ii) Mg/Mn ordering in olivine MgMnSiO4, and (iii) La3+/M2+ order-disorder in the quaternary cuprates La2MCu2O6 (M = Ca, Sr). These examples include the interchange of atoms in a system where only short-range forces need to be considered, the Interchange of isovalent ions, and the interchange of heterovalent ions, respectively. The importance of relaxation effects increases in the order i-iii, i.e., as the size/charge mismatch between the interchanged atoms or ions increases.