The picosecond CO2 gas laser has proven a valuable tool in strong-field physics applications. We review the merits of this approach, taking as an example, the Brookhaven Accelerator Test Facility (ATF) that affords a platform for exploring novel methods of particle acceleration and radiation sources. To carry out this mission, the ATF is equipped with a picosecond terawatt CO2 laser system, PITER-I. We describe the physical principles and architecture of this multi-stage laser system and its application in two high-energy physics projects. The first is the intense Thomson scattering of the CO2 beam from 60 MeV electrons with production of one x-ray photon per electron that opened the possibility for a Compton gamma-source generating a polarized positron beam for the next generation of electron-positron colliders, such as the International Linear Collider (ILC) and the Compact Linear Collider (CLIC). The second is our new study of a high-brightness multi-MeV ion- and proton-beam source energized by this picosecond CO2 laser. High-energy, collimated particle beams originate from the rear surface of the laser-irradiated foils. The expected advantage from using a CO2 laser for this application, rather than an ultra-fast solid state laser, is the 100-fold increase in the electron ponderomotive potential due to the tenfold longer wavelength of the CO2 laser. This innovation promises to substantially enhance energy efficiency and particle yield, and will facilitate the advancement of laser-driven ion accelerators towards practical applications. Finally, we address possibilities for generating CO2 laser pulses of petawatt peak power and a few-cycles duration.