The book proposes several types of Mittag-Leffler and exponential Euler differences for different types of differential equations, such as FODEs in the Caputo sense and CFOEs, by using the variation-of-constants formulas in nonlocal calculus. From the point of view of the theory of differential equations, some basic theories are set up for the further study of the differential equations generated by the Mittag-Leffler and exponential Euler differences. In addition, some important dynamic properties are studied in this book, such as the well-posed problems, global exponential stability, global exponential synchronization, almost automorphism, and so on. It lays certain theoretical foundations for future research on the Mittag-Leffler and exponential Euler difference models and opens up a new research area in the theories of numerical computations and difference equations.