Classical theories of explosion for isolated reactant particles are extended to cover the cases of reactant particles embedded in an inert (chemically) and a reactive matrix. In these cases the heat released or absorbed by particles influences the heat released or absorbed in the matrix. The critical conditions for ignition in the particles and matrix may be expressed in terms of the dimensionless groups of the classical theory psi and delta as well as some other important parameters such as beta, gamma or Bi-ov, which relate the physical properties of the particles and matrix. The different boundary conditions such as the Semenov boundary condition (uniform internal temperature systems) and the Frank-Kamenetskii boundary condition (distributed internal temperature systems) are investigated. Approximate solutions besides the exact ones are used in this study. Important results are obtained showing the effect of thermal interaction between particles and matrix.