This study presents an exhaustive review on modelling and analysis of multi-directional graded (beam/plate/shell) structures. From the past few decades, a significant increase in publications and research activities are noticed in the field of functionally graded composite structures due to their high strength and stiffness, flexibility in design and greater features over conventional composites. However, most of the studies reported on functionally graded structures are confined to a unidirectional gradation of material constituents. Now, many applications are demanding functionally graded structures with multi-directional material properties in which material properties vary in two or more directions, to meet the multi-functional requirements. In this review article, various micromechanical material modelling for unidirectional and multi-directional graded materials are presented and an effort has been made to include research studies reported on multi-directional functionally graded beam, plate and shell structures with an emphasis on work published since 2000. In addition, on the basis of the reviewed literature, concluding remarks are presented to showcase the future directions in this research field. © 2020 Elsevier Ltd