Recursive functions on context-free languages (CFRF) are a kind of new recursive functions proposed especially for describing non-numerical algorithms used on computers. An important research aspect of this kind of functions is the exploration of evaluation algorithms. The paper summarizes the author’s research on this issue. Beginning by a discussion on possible combinations of calculation and parsing, it presents a comprehensive introduction to the major algorithms in an order in which the applicable ranges of the algorithms increase (this is also the order that the algorithms were devised). The introduction emphasizes on a new, efficient, and general evaluation algorithm, i.e. the tree-oriented evaluation algorithm. The paper also explains the evaluation method for the many-sorted recursive functions extended from CFRF. The algorithms of CFRF have been realized on computers, and have been validated by practice.