This paper reports on the existing robot force control algorithms and their composition based on the review of 75 papers on this subject. The objective is to provide a pragmatic exposition with speciality on their differences and different application conditions, and to give a guide of the existing robot force control algorithms. The previous work can be categorized into discussion, design and/or application of fundamental force control techniques, stability analysis of the various control algorithms, and the advanced methods. Advanced methods combine the fundamental force control techniques with advanced control algorithms such as adaptive, robust and learning control strategies.