The book "Variable-Order Fractional Calculus of Variations" is a specialized text that focuses on the study of fractional operators with variable order, particularly in relation to variational problems involving variable-order operators. It presents a new numerical method for solving differential equations that include Caputo derivatives of variable order. Three typical Caputo fractional operators are examined, for each of which an approximation formula in terms of standard derivatives (of integer order) is derived. Additionally, estimates for the error of these approximations are provided. The authors analyze variational problems characterized by one or more constraints, where the functional depends on a combined Caputo derivative of variable fractional order. Necessary optimality conditions of the Euler-Lagrange type are also established. This book serves as a valuable resource for researchers in mathematics, physics, engineering, control, and optimization, offering both analytical and numerical methods for addressing variational problems.