Creativity is part and parcel of human history and enables (groups of) individuals to adapt to and shape their natural and social surroundings. Here we identify (1) core functions of creativity ("what is it for?") in terms of its ability to solve ill-defined problems of survival and prosperity and, (2) the neurocognitive mechanisms ("how does it work?") underlying creative production in terms of cognitive persistence and flexibility. We summarize experimental support for this Dual Pathway to Creativity Model (DPCM) from our own laboratory and that of others, and review work implicating the dopamine-innervated fronto-striatal circuitry in achieving a balance between cognitive flexibility on the one hand, and persistence on the other. We use DPCM to analyze how creativity emerges and develops across the lifespan. We show (3) how personalities and psychopathologies marked by approach (avoidance) motivation link to creativity because of enhanced capacity for flexibility (persistence), and (4) how socio-cultural factors, including psychological safety, diversity, and leadership, condition individual and group creativity. We conclude with open questions for future research, including how (5) individuals and groups move from generating to implementing creative ideas, insights, and problem solutions.