The development, implementation, variant, and future directions of a new swarm intelligence algorithm, brain storm optimization (BSO) algorithm, are comprehensively surveyed. Brain storm optimization algorithm is a new and promising swarm intelligence algorithm, which simulates the human brainstorming process. Through the convergent operation and divergent operation, individuals in BSO are grouped and diverged in the search space/objective space. To the best of our knowledge, there are 75 papers, 8 theses, and 5 patents in total on the development and application of the BSO algorithm. Every individual in the BSO algorithm is not only a solution to the problem to be optimized, but also a data point to reveal the landscape of the problem. Based on the developments of brain storm optimization algorithms, different kinds of optimization problems and real-world applications could be solved.