As the well is being drilled, formation fluid flows into the wellbore and up to the surface.
Sometimes an inert gas is injected into the drilling mud to reduce its equivalent density and hence its hydrostatic pressure throughout the well depth.
Because air is compressible mud pulse telemetry measurement while drilling (MWD) tools which require an incompressible fluid can not work.
Corrosion is also a problem, but can be largely avoided using a coating oil or rust inhibitors.
References Nas, Steve, Chapter 12 Underbalanced Drilling, from Petroleum Engineering Handbook, Volume II, Editor Robert Mitchell, 2007, pages II-519 to 569.