Matrix Switches
In addition to patch bays, another popular method for interfacing different pieces of equipment is matrix switches. Originally called crossbar or crosspoint switches these have been around since the 1800s, where they were used to route telegraph lines.
Essentially matrix switches have the various inputs on one axis and the outputs on the other. The connection points form a grid or matrix. In order to connect an output to an input, an electrical connection is made at the intersection of those ins and outs. Many of the newer matrix switches have a digital display and the connections are made by simply entering the coordinates from a keypad.
A matrix arrangement can even be found on a typical analog mixing console that has the aux sends and output busses arranged vertically with the input faders arranged horizontally. In this case, either pushing a button or turning up the gain on the send makes the connection to that particular bus. Virtual mixers are arranged the same way with the various bus sends on all or selected input.
In fact, the first electronic computer RAM was a matrix switch, where a ring of ferrite material surrounded each intersection of a matrix of wires. The ferrite would become magnetized and go from a 0 (not-magnetized) state to a 1 (magnetized) state when a current passed through the ring on both intersecting wires at once.