The XBAND Video Game Modem and Network allowed owners of Sega Genesis and Super Nintendo game systems to play head-to-head over a phone line in 1994, before "twitch" gaming over the Internet was feasible. How was this accomplished?
Many games played over the Internet today use a client-server model, where the server has a full copy of the game state, and distributes appropriate pieces to the connected clients. Due to the technology available in 1994, XBAND couldn't work this way.
When the user wanted to play a game online, the modem called the server through a local dial-up point-of-presence, and requested a match for the currently-installed cartridge. The server either told the modem to wait for a connection, at which point it would sit and wait for the phone to ring, or told it to dial the other player's phone number. Once connected, the game consoles communicated directly, removing client-server communication latency from the equation.
The games ran in lockstep on each console. The cartridges had to be exactly the same, as any difference in logic could throw the systems out of sync. (In a couple of cases, publishers quietly released an updated version of a cartridge.) All game state, including the random number generator seed, had to be synchronized at the start. Once game play began, the consoles simply exchanged controller reads. At 2400bps, there was just enough time to send a bitmap of currently-pressed buttons and some error-correction redundancy at 30 fps.
While faster modems were available at the time, the slower modems were less expensive, had sufficient throughput, and had better latency characteristics. Features like data compression and error correction were disabled to avoid introducing additional latency.
An attempt to reduce the latency even further was attempted but never shipped. By changing video modes on the Genesis, the television's VSYNC phase could be altered, potentially allowing two independent televisions to be brought (temporarily) into sync with each other.
An hour-long documentary on Catapult and XBAND can be found on youtube.