In this paper, we give a survey of multi-structured designs and their various applications. Multi-structured designs are block designs with additional structure imposed on the blocks. Combinatorial conditions of the further block structure depend on applications. Examples of multi-structured designs are nested designs, row-column designs, splitting design, etc. Their constructions have been independently studied for a long time and often use similar techniques. Cyclic multi-structured designs are related to various types of sequences which have many applications to modern communications. The paper consists of three parts. The first part deals with classical multi-structured designs which are used in experimental designs and authentication systems. The second part reviews several applications to optical and wireless communications which use cyclic multi-structured designs. Finally, in the third part, we discuss algebraic and geometric construction methods which are commonly used for many types of multi-structured designs.