The central half kiloparsec of the Milky Way: The Central Molecular Zone (CMZ) is an energetic region, containing a supermassive black hole, multiple super star clusters, 10% of the molecular gas in the entire Galaxy, and potentially the launching point of giant relic outflows detected in gamma rays. The juxtaposition of all of these sources combined with the observational challenge of peering through our Galaxy edge-on to expose this region means that our picture of the CMZ is constantly evolving as new discoveries are made, and improved observational techniques allow for refinement of past results. I will begin this review by summarizing the current knowledge of the CMZ, concentrating upon changes to our understanding of this region since the last major literature review two decades ago. The primary focus of this review will be the molecular gas in the CMZ, specifically the physics responsible for its extreme temperature, density, and turbulence, and the role this gas plays as a reservoir for future star formation and feeding of the supermassive black hole. I will highlight a burst of new interest in this region in the past 5 years, including numerous surveys in progress, and new opportunities to address longstanding mysteries in this region that are being enabled by current and future observatories. Much of this interest is driven by a new focus on the environment of molecular gas and how it may influence the star formation process in extreme sources like high-redshift galaxies. As the most extreme environment for star formation in our Galaxy, the center of our galaxy is observed to have many properties in common with those of high-redshift galaxies. This provides a unique opportunity to understand the small-scale physics at play in the molecular gas at the peak of star formation and galaxy assembly, which cannot otherwise be resolved. I will conclude this talk by discussing several areas of research I am actively engaged in, to address the outstanding questions about gas properties in the CMZ, and calibrate its use as a proxy for understanding the early universe.