This paper is an extended survey of results established by the author in some his previous works and recalled at the end of every Section. Section 2 deals with the concepts of upper and lower inverse of a fuzzy multivalued function, useful to define the hemicontinuity of such mappings [cf.J. Appl.Math.Stochastic Anal.12, No.1, 17–22 (1999; Zbl 0926.47056)]. Section 3 contains the fuzzy version of the closed graph theorem for fuzzy multivalued functions [cf.Fuzzy Sets Syst.115, No.3, 451–454 (2000; Zbl 0988.54009)]. Section 4 is dedicated to the study of the concepts of union, intersection and composition of a family of fuzzy multivalued functions. Their relationships with the concept of hemicontinuity is established and the fuzzy maximal principle is also deduced [cf.J. Fuzzy Math.11, No.4, 945–954 (2003; Zbl 1137.90754)]. In Section 5, properties of vector-valued fuzzy multivalued functions are given. In particular, the concepts of convex hull and demicontinuity are studied [cf.J. Appl.Math.Stochastic Anal.14, No.3, 275–282 (2001; Zbl 0994.47076)]. Section 6 seeks to define the intersection convolution of two fuzzy multivalued functions assigned over two groups. Fundamental properties are established, mainly the theorem on the existence of the extension of linear selector fuzzy multivalued functions under suitable assumptions [cf.J. Comput.Anal.Appl.6, No.2, 125–137 (2004; Zbl 1095.47058); Ital.J.Pure Appl.Math.17, 83–90 (2005; Zbl 1137.47309)]. Section 7 contains results on fuzzy order preserving selectors for fuzzy multivalued functions: in particular, the author shows that such a selector exists under suitable conditions and a related fixed point theorem is also given [cf.J. Fuzzy Math.9, No.1, 97–101 (2001; Zbl 0978.03043)]. In Section 8, the author studies the operations of addition and scalar multiplication for linear fuzzy multivalued functions, establishing various results [cf.J. Fuzzy Math.9, No.1, 127–137 (2001; Zbl 1027.47080)]. The concluding Section 9 deals with the existence of fixed points of fuzzy multivalued functions with values in fuzzy ordered sets [cf.J. Fuzzy Math.6, No.1, 27–131 (1998; Zbl 0909.47055)].