This article discusses the impact of artificially intelligent computers to the process of design, play and educational activities. A computational process which has the necessary intelligence and creativity to take a proactive role in such activities can not only support human creativity but also foster it and prompt lateral thinking. The argument is made both from the perspective of human creativity, where the computational input is treated as an external stimulus which triggers re-framing of humans’ routines and mental associations, but also from the perspective of computational creativity where human input and initiative constrains the search space of the algorithm, enabling it to focus on specific possible solutions to a problem rather than globally search for the optimal. The article reviews four mixed-initiative tools (for design and educational play) based on how they contribute to human-machine co-creativity. These paradigms serve different purposes, afford different human interaction methods and incorporate different computationally creative processes. Assessing how co-creativity is facilitated on a per-paradigm basis strengthens the theoretical argument and provides an initial seed for future work in the burgeoning domain of mixed-initiative interaction.