The primary mission of the Viking project, with two orbiters and two landers at Mars, was completed in November 1976, but operations have since been extended in a series of stages, and they are still continuing as of November 1979. The lander investigations that searched for evidence of living organisms and organic chemicals in the surface material and determined the chemical composition of the atmosphere were completed early in 1977. Since then a major emphasis has been on the study of the weather on Mars, with instruments on all four spacecraft contributing. The acquisition of samples for the inorganic analysis of surface material, the manipulation of the sampling tool to investigate the physical and magnetic properties of the surface, and the seismic measurements were terminated a year later, but other investigations were continued. Orbiters and landers have acquired large quantities of photographs of the surface and of atmospheric phenomena. Viking Orbiter 2 ceased to operate in July 1978; Viking Orbiter 1 was shut down temporarily in February 1979 but resumed operations in July for an additional 3 months or more. Both landers have been programmed to continue for another decade, but only Viking Lander 1 will yield scientific data. This paper discusses the operation and chronology of the Viking mission. The scientific results are discussed in a companion paper.