The present review on inclusion problems emphasizes papers primarily published after 1982. Materials associated with inclusions are composite materials, precipitated or transformed alloys, porous media, and polycrystals. The inclusion problems deal with the following subjects of these materials: (1) stress fields caused by non-elastic strains (eigenstrains) and; (2) stress disturbances due to heterogeneity and inhomogeneities of materials under applied stresses; (3) average elastic moduli and average thermal properties; (4) nonelastic constitutive equations; (5) behavior of inclusions including nucleation, growth, and collapse of voids; (6) cracks and inclusions including the transformation toughening, crack growth through composites and stress intensity factors; (7) sliding and debonding inclusions; and (8) dynamic effects of inclusions. The present review is an update to the review paper, which appeared in Applied Mechanics Reviews, Volume 41 (1988), and includes opinions of some of the experts who made significant contributions to the field of inclusion problems. It is our hope that we cited all the important papers relevant to the subject of inclusion problems. The first author would welcome anyone’s comments and any references which were not included in this review.