This chapter is mainly concerned with the determination of general relationships between microscopic and macroscopic mechanical properties for elastoplastic material with or without damage. The overall properties are determined in terms of the unknown properties of each constituent phase of the heterogeneous body. At first we must define a representative volume element (RVE) of the heterogeneous material for which the macroscopic mechanical fields are some spatial average of the microscopic one. The determination of local quantities is achieved by solving some particular boundary value problem on the RVE, from which macroscopic quantities are derived. The essential structure of micro-macro relationships is presented in the case of elastoplastic material. A generalisation is given to take the temperature field into account. We present also a model of damage and its averaging process. Finally we discuss the determination of macroscopic temperature through continuum thermodynamics.