The continents are fixed in place, or at most move very slowly without a fully accepted mechanism.
Plate tectonics became the consensus framework in earth sciences in 1966–1968, following J. Tuzo Wilson's transform fault concept and rapidly accumulating paleomagnetic evidence. This was geology's equivalent of the Darwinian revolution.
What changed?
For most of geological history as a discipline, the science of the solid Earth was a science of classification and description. Geologists mapped formations, identified strata, named minerals. What they did not have, well into the 1960s, was a unifying theory to explain why mountains existed where they did, why earthquakes clustered along specific lines, why certain rock types appeared on opposite sides of oceans thousands of miles apart. The standard explanation was isostasy and slow cooling, the crust settled, cracked, and rose as the Earth lost heat from its molten formation. The continents were fixed; the ocean basins permanent.
Alfred Wegener had challenged this picture in 1912 with his hypothesis of continental drift. His argument was simple: the coastlines of South America and Africa fit together with the precision of torn newspaper, fossil species matched across oceans unbridged by land, and glacial deposits from a Carboniferous ice age appeared in regions now near the equator. Wegener proposed a supercontinent, Pangaea, that had fragmented and whose pieces had slowly drifted apart. The geological establishment was not persuaded. Without a mechanism, continental drift was a just-so story; the forces Wegener invoked to push continents through oceanic crust were geophysically absurd.
The mechanism came from the sea floor. During World War II, the US Navy had equipped vessels with sonar to hunt enemy submarines, and in doing so generated detailed maps of the ocean floor for the first time. What emerged was startling: every ocean basin contained a continuous underwater mountain range, the mid-ocean ridge system, running tens of thousands of miles. Harry Hess, a Princeton geologist who had commanded a Navy vessel during the Pacific campaign, synthesised the data into the seafloor spreading hypothesis in 1960 and 1962: hot magma wells up continuously at the ridges, solidifies, and pushes the ocean floor outward like a conveyor belt, carrying the continents with it.
Confirmation came from magnetism. As lava hardens at mid-ocean ridges, it locks in the orientation of Earth’s magnetic field at that moment. Earth’s field reverses periodically, so the spreading seafloor records a history of reversals, and because new crust forms symmetrically on both sides of a ridge, the pattern should mirror itself. In 1963, Fred Vine and Drummond Matthews at Cambridge demonstrated that the magnetic stripes in the North Atlantic seafloor matched exactly. J. Tuzo Wilson’s 1965 paper introducing the concept of transform faults completed the geometric picture. By 1966 the scientific debate was effectively over. Plate tectonics had become the framework within which all other geological questions would be asked.