Legendre polynomials and, respectively, Legendre functions are one of the most important functions in physics. In this chapter, we will discuss and derive corresponding program codes supporting complex arguments and complex indices. The code is freely available. The functions covered are Legendre polynomials and Legendre functions of first and second kind, the evaluation of the nodes for the Legendre functions of first kind based on the corresponding Jacobi matrix, the Mehler or conical functions, the toroidal or ring functions, and others. An application is, e.g., the evaluation of spherical harmonics. In dependence of the function arguments and the function indices, the evaluation will be based either on recurrence relations or on hypergeometric functions.