Here, the independent variable is discrete rather than continuous. The chapter starts with a preliminary section that synthesises the basic techniques generally used to solve recurrence equations. In particular, ordinary generating functions (OGF) and exponential generating functions (EGF) are introduced as useful tools to solve linear recurrence equations with varying coefficients. Their limit is underlined, both in terms of applicability and interpretability, and asymptotic techniques come as a powerful remedy to these shortcomings. The general asymptotic reasoning that organised the preceding chapters is applied to the present context: multiple-scale and WKB techniques are developed for discrete problems. A technique described as “peeling off factorials” is presented. In addition, Euler–Maclaurin summation and techniques of acceleration of convergence such as Richardson’s method and Shanks transformation are exposed.