This paper is an extensive survey of the Bee Colony Optimization (BCO) algorithm, proposed for the first time in 2001. BCO and its numerous variants belong to a class of nature-inspired meta-heuristic methods, based on the foraging habits of honeybees. Our main goal is to promote it among the wide operations research community. BCO is a simple, but efficient meta-heuristic technique that has been successfully applied to many optimization problems, mostly in transport, location and scheduling fields. Firstly, we shall give a brief overview of the other meta-heuristics inspired by bees’ foraging principles pointing out the differences between them. Then, we shall provide the detailed description of the BCO algorithm and its modifications, including the strategies for BCO parallelization, and giving the preliminary results regarding its convergence. The application survey is elaborated in Part II of our paper. [Projekat Ministarstva nauke Republike Srbije, br. OI174010, br. OI174033 i br. TR36002]