Nokia has achieved a connection speed of 5Gbps—about 625MB/sec—over 70 metres of conventional twisted-pair copper telephone wire, and 8Gbps over 30 metres. The trial used a relatively new digital subscriber line (DSL) protocol called XG.fast (aka G.fast2).
XG.fast is the probable successor of G.fast, which was successfully trialled in a few countries over the past couple of years and will soon begin to commercially roll out. (In an unusual turn of events, the UK will probably be the first country with G.fast.)
Fundamentally, both G.fast and XG.fast are best described as "VDSL on steroids." Basically, while a VDSL2 signal frequency maxes out around 17MHz, G.fast starts at 106MHz (it can be doubled to 212MHz) and XG.fast uses between 350MHz and 500MHz. This means that there's a lot more bandwidth (the original meaning of the word), which in turn can be used for transferring data at higher speeds.
By way of example, VDSL2 can do around 100Mbps over that 17MHz channel; G.fast can do about 700Mbps at 106MHz; and XG.fast can go all the way up to 10Gbps at 500MHz with two bonded telephone lines.