That group brainstorming increases creativity can be considered a truism. And yet; there is overwhelming evidence that group brainstorming produces fewer ideas, and fewer good ideas than individual brainstorming. This article reports on two research programs which succeeded in identifying the causes of this productivity loss and explaining the psychological processes which mediate it. In the early studies, Diehl and Stroebe (1987, 1991) identified mutual production blocking as the main cause. Later Nijstad, Stroebe and Lodewijkx (2002, in press) developed a cognitive theory of idea generation (SIAM; Search for Ideas in Associative Memory), to explain why group members are unable to use productively the waiting periods due to "turn-taking". According to this theory, idea generation consists of two phases, with problem-relevant knowledge being activated in a first phase, followed by idea-generation in a second phase. According to SIAM, production blocking should affect both phases, with lack of predictability of the waiting periods inhibiting the more effortful knowledge activation process, and length of waiting periods interfering with idea generation. Two experiments are reported to support these predictions. The last section derives and tests predictions from SIAM about conditions under which exposure to ideas (in the absence of blocking) could stimulate idea generation. Key words: brainstorming, creativity, group productivity, group processes, social cognition.