Predictions concerning development, interrelations, and possible independence of working memory, inhibition, and cognitive flexibility were tested in 325 participants (roughly 30 per age from 4 to 13 years and young adults; 50% female). All were tested on the same computerized battery, designed to manipulate memory and inhibition independently and together, in steady state (single-task blocks) and during task-switching, and to be appropriate over the lifespan and for neuroimaging (fMRI). This is one of the first studies, in children or adults, to explore: (a) how memory requirements interact with spatial compatibility and (b) spatial incompatibility effects both with stimulus-specific rules (Simon task) and with higher-level, conceptual rules. Even the youngest children could hold information in mind, inhibit a dominant response, and combine those as long as the inhibition required was steady-state and the rules remained constant. Cognitive flexibility (switching between rules), even with memory demands minimized, showed a longer developmental progression, with 13-year-olds still not at adult levels. Effects elicited only in Mixed blocks with adults were found in young children even in single-task blocks; while young children could exercise inhibition in steady state it exacted a cost not seen in adults, who (unlike young children) seemed to re-set their default response when inhibition of the same tendency was required throughout a block. The costs associated with manipulations of inhibition were greater in young children while the costs associated with increasing memory demands were greater in adults. Effects seen only in RT in adults were seen primarily in accuracy in young children. Adults slowed down on difficult trials to preserve accuracy; but the youngest children were impulsive; their RT remained more constant but at an accuracy cost on difficult trials. Contrary to our predictions of independence between memory and inhibition, when matched for difficulty RT correlations between these were as high as 0.8, although accuracy correlations were less than half that. Spatial incompatibility effects and global and local switch costs were evident in children and adults, differing only in size. Other effects (e.g., asymmetric switch costs and the interaction of switching rules and switching response-sites) differed fundamentally over age.