The star formation rate in the central 500 pc of the Milky Way is lower by a factor of > 10 than expected for the substantial amount of dense gas it contains, which challenges current star formation theories. I discuss which physical mechanisms could be causing this observation and put forward a self-consistent cycle of star formation in the Galactic center, in which the plausible star formation inhibitors are combined. Their ubiquity suggests that the perception of a lowered central SFR should be a common phenomenon in other galaxies with direct implications for galactic star formation and also potentially supermassive black hole growth. I then describe a scenario to explain the presence of super star clusters in the Galactic center environment, in which their formation is triggered by gas streams passing close to the minimum of the global Galactic gravitational potential at the location of the central supermassive black hole, Sgr A*. If this triggering mechanism can be verified, we can use the known time interval since closest approach to Sgr A* to study the physics of stellar mass assembly in an extreme environment as a function of absolute time. I outline the first results from detailed numerical simulations testing this scenario. Finally, I describe a study showing that in terms of the baryonic composition, kinematics, and densities, the gas in the Galactic center is indistinguishable from high-redshift clouds and galaxies. As such, the Galactic center clouds may be used as a template to understand the evolution (and possibly the life cycle) of high-redshift clouds and galaxies.