The cycle of star formation governs the evolution of galaxies. In some local galaxies, the star formation rate in their centers are much higher than other normally star-forming galaxies and may be more similar to galaxies at earlier cosmic times. I present observational results from two archetypal nearby starburst galaxies: NGC253 and M82. First, I will discuss how gas flows to the center of NGC253 along its bar to fuel the extreme burst of star formation. Using very high spatial resolution data from ALMA tracing emission from dust and dense molecular gas, we find that the massive, compact, very young “super” star clusters (SSCs) found in the center of NGC253 are arranged in a ring. Moreover, we find that the SSCs and dense molecular gas are found at the innermost orbit predicted by the barred potential of this galaxy, as expected. I will also show new data on the SSCs in M82 revealed by JWST NIRCam images. Next, I will discuss the detection of massive outflows of molecular gas detected from three of the SSCs in NGC253. These outflows carry a substantial fraction of the gas mass away from the clusters and may stop these clusters from growing even larger. The precise physical mechanism powering these outflows is uncertain, but winds from massive stars and dust-reprocessed radiation pressure are the best candidates - different from lower mass, less extreme star clusters. Finally, I will discuss the result of an extreme burst of star formation on the host galaxy: the central starbursts in both NGC253 and M82 are driving galaxy-scale, multiphase superwinds. Together, these new observations of NGC253 and M82 paint a more complete picture of gas feeding and feedback in extreme star-forming environments and set the stage for JWST observations coming in Cycle 1.