A survey of experimental and theoretical results on physics of a CO laser operating on first-overtone (FO) vibrational transitions V plus 2 implies V is presented. A special attention is paid to quite new results recently obtained at the P. N. Lebedev Physics Institute (Russia), TRINITI (Russia) and Air Force Research Lab. (USA). Efficient multiwavelength pulsed FO CO lasing with output efficiency up to 11% and specific output energy up to 50 J/l Amagat is observed within the spectral range of 2.5-4.1 micrometers corresponding to the vibrational transitions V plus 2 implies V from 6 implies 4 up to 37 implies 35. Single-line frequency tunable FO CO lasing on the wavelengths from approximately 2.7 up to 4.2 micrometers with the maximum output efficiency up to approximately 1% is also observed. Multiline and single-line lasing on 430 ro-vibrational lines is obtained. Theoretical calculations based on the experimental data predict that multiline FO CO laser efficiency can be enhanced up to 20%. The effect of spectrum alternation, i.e., an alternation of strong and weak vibrational bands, in pulsed FO CO laser spectrum, which is determined by two sets of cascade transitions, is experimentally observed for the first time. An influence of nitrogen on spectral characteristics of a single-line FO CO laser operating on very high vibrational transitions up to 38 implies 36, which is related to quasi-resonance overlapping of the transition with 0 implies 1 transition of nitrogen molecule, is discussed. High efficiency and high specific output energy places the FO CO laser amongst other high-power lasers such as CO2 laser, fundamental band CO laser and HF(DF) laser.