Creativity is typically defined as producing something that is novel, useful, and surprising. Such endeavor plays a critical role in the arts and scientific discovery. However, not all creativity is groundbreaking or historically important. As a common cognitive activity, creativity is amenable to scientific investigation leading to a process-based understanding, so it should be possible to propose models and write computer programs simulating the creativity process. However, the path from cognitive models to computational models is still not trodden as often as would be beneficial. This chapter reviews common concepts underlying many computational creativity efforts, namely idea generation, search, and evaluation. Two example computational models are described in more detail, namely the explicit-implicit interaction theory and the CreaCogs architecture. The chapter concludes with a discussion of current shortcomings and future directions for computational creativity as well as discussing promising avenues and successes of current models.