Much of what we know about the process of star formation comes from observations of our own Milky Way and of nearby spiral galaxies. However, this sample only probes a relatively narrow range of galaxy properties and thus does not provide an effective test of how galaxy properties like mass, metallicity, and star formation rate affect star formation. Fortunately, with the advent of new telescopes like ALMA, GBT, and JWST, we are opening up new frontiers in the study of star formation by extending detailed studies to more distant and less massive galaxies than previously possible. In this talk, I will present two examples of how the capabilities of new instrumentation are driving extragalactic star formation studies. First, I will show how deep single dish surveys of nearby galaxies enabled by multi-pixel feeds such as ARGUS on the GBT allow us — for the first time — to map the dense molecular gas more closely associated with star formation in large samples of nearby galaxies. Second, I will present ALMA observations of the molecular gas in the prototypical nearby blue compact dwarf galaxy II Zw 40. These observations represent the first giant molecular cloud scale observations in a blue compact dwarf galaxy and allow us to compare the properties of its molecular clouds to those in other, less extreme systems. Finally, I will highlight possible future extensions of these projects using JWST and ALMA.