Swiss company Omega has been the official Olympic timekeeper on 25 occasions since the 1932 Games in Los Angeles, where as the first such timekeeper they supplied 30 stopwatches.
Previously, officials simply turned up with their own stopwatches. Omega was able to supply stopwatches that could time to a 1/10 of a second, which was twice as good as earlier watches.
Technology has moved on since then in many ways to enable more accuracy and extra features, as explained on Omega's Highlights of Olympic timekeeping website.
That site points out a number of firsts. These include the first photo finish camera, in 1949; the first electronic timer to be used in 1952 Games in Helsinki; in 1961 enabling the times of competitors to be superimposed on television screens; the 1968 Games in Mexico City the first to have all-electronic timekeeping in all sports, hence no more officials holding stopwatches; the 1984 Games in Los Angeles was the first with pressure-sensitive false start recorders for athletics and swimming together with loudspeakers for the starting signal behind each block; GPS was first used for sailing in the 1996 Games in Atlanta; and Sydney in 2000 was the first with real-time results going up on the Internet.
Using touch or contact-pads in the Olympics to record officially accepted times in swimming dates to the 1968 Games at Mexico City.
Previously, each lane had three judges standing at the end of the pool to record the times of each swimmer with stop watches plus presiding judges, who would watch from the side. In the 1960 Games in Rome, there was a problem deciding on the results in the 100 meter free-style swim. John Devitt of Australia and Lance Larson of the USA finished almost together, but most of the audience, the sports reporters, and Larson’s jubilant pose as seen in photos suggested that the American had won. Devitt even congratulated Larson.
The three judges in Larson’s lane gave him a faster time than those in Devitt's lane, yet the presiding judges ruled that Devitt had won with an identical time to Larson – 55.2 seconds.
This was despite the evidence of the backup, non-official electronic system. This recorded 55.10 for Larson and 55.16 for Devitt.
Perhaps to prevent such a problem recurring, Omega developed improved technology to ensure that electronic timing would be regarded as acceptable. The earlier attempts, according to the Omega patents, involved the swimmers touching pneumo-electric tubes which would send a signal. They were described as expensive, high-maintenance, complicated and slow. You also had to make quite a lot of pressure for the system to be activated. The system used at Rome was presumably along these lines.
The new system involved compressible contact cables that would send an electric signal, with the patent titled Finishing-contact system for timekeeping competitions. No doubt it has been improved since.
However, a problem emerged in the 2008 Games at Beijing. The American Michael Phelps beat Serb Milorad Cavic in the 100 metres butterfly by 0.01 of a second. Underwater photographs taken 1/1000 of a second apart were used to determine that although Cavic touched the wall first, Phelps still won. The contact pad was 12 mm thick. To register a finish, the swimmer had to push it in to a depth of 2 mm. Apparently Phelps had been told how the technology worked, and had pushed sufficiently hard. Again there was a problem with activating the system, as noted all those years ago by Omega.
This is a list of (mostly) relevant US patents by Omega for recording times etc.