The importance of fuzzy calculus becomes strongly evident if one thinks of the role played by classical calculus concepts in the mathematical modeling of real-world phenomena. There is an imprecision or vagueness often characterizing the gathered experimental information or even the theoretical background needed to quantitatively describe a particular natural phenomenon. This chapter first defines fuzzy functions and their properties and then examines their integration and differentiation. It proceeds with the definition of a nonfuzzy function with constraints on the fuzzy domain and the fuzzy codomain. Thereafter, the chapter considers a theory of fuzzy limits, and finally, looks at fuzzy differential equations. It focuses on the approach of Mark Burgin based on the notion of the fuzzy limits of sequences and developed in the frame of neoclassical analysis, that is, the study of ordinary (real) functions on the basis of fuzzy set theory, and set-valued analysis.