Orogeny, or orogenesis, is the term earth scientists use for the creation of mountains. It is a rather small word for something that describes titanic forces.
Mountains form at places where the Earth's crust is battered by movement of the tectonic plates making up the top few tens of miles of the planet. According to the theory of plate tectonics, thin layers of the crust are very slowly moving in different directions. Most mountain ranges form along the long, linear zones where two plates meet.
Many of the most familiar mountain ranges have formed where the net movement of two plates is toward each other, like two cars colliding head-on. If one plate is continental, such as South America, and the other is oceanic, like the Pacific Ocean, the denser oceanic crust bends downward to slide under the continental crust, a process called subduction. Subduction is possible because the layer of the Earth below the crust is not rigid and brittle like the rocks at the surface, but behaves more like an extremely viscous liquid.
As the oceanic crust sinks deeper, it begins to melt. This sort of plate interaction is usually "wet," or marked by volcanic activity as melted oceanic crust rises back to the surface. Most of the Pacific Plate is surrounded by these subduction zones, creating what is often called the "Ring of Fire." Along the west coast of South America, the Ring of Fire volcanoes are part of the Andes Mountains volcanic arc. Volcanic arcs at a subduction zone are underlain at depth by a magma chamber filled with molten rock that eventually cools to form a batholith, intrusive igneous rocks such as granite. The Sierra Nevada of California is one such granitic batholith.
Continental crust is affected by collisions, too. The immense pressures created by the collision push rocks from the edge of the continent inland in long, thin sheets called thrusts. This "thin-skinned" deformation pushes stacks of rocks for tens or hundreds of miles inland, often folding them like sheets of newspaper or a rug that's been pushed from an edge. Fold mountains like these dominate mountain ranges such as the Andes, Canadian Rockies and Alps. Often, the folded mountains are eventually penetrated by volcanoes.
When two continents collide, the collision batters both edges and creates huge stacks of folded, faulted rocks. Continent-continent collisions are occurring in Iran (the Zagros Mountains) and, most prominently, where the Indian subcontinent is forcing its way into the underbelly of Asia. The highest mountains in the world, the Himalayas, are a result of this latter collision. Continent-continent collisions are more likely to be dry, having less volcanism than in zones where oceanic crust is subducting.
Tectonic plates sometimes move away from each other, causing a different sort of orogenesis. As the plates pull apart, hotter material deeper in the earth rises to fill the gap formed between them. Counterintuitively, this hot material causes the thinned crust to expand and bulge upward even as the adjacent plates move apart.
The breakup results in so-called thick-skinned deformation: the brittle rocks at the surface cannot stretch, so they break along surfaces that curve and flatten toward the centerline of the expansion. Large blocks of rock slowly slide down those surfaces, or faults, rotating as the fault flattens. In combination with the thermal bulge, the rotated chunks of crust create raised fault-block mountains, usually separated by broad basins full of detritus eroded from the rotated blocks. This pattern is typical of rift zones such as the Rio Grande Valley of New Mexico and Colorado or Olduvai Gorge in Africa. Volcanism is common within this environment as well, although the chemistry of the rocks differs from that of rocks formed over subduction zones.
Some mountain ranges occur in the otherwise quiet middle of continental and oceanic plates. These are purely volcanic ranges centered on a "hot spot" where convection currents in the Earth's mantle conduct heat away from the molten core. The best example of these hot spot or "plume" ranges is the Hawaiian Island chain, which comprises a line of active and extinct volcanoes that record the position of the Pacific tectonic plate relative to a mantle hot spot.
Earth scientists understand orogeny within the framework of plate tectonics. As scraps of crust slowly move around the Earth's surface, mountains form where they jostle against each other or where they are ripped apart. The process, however, is slow: those plates move at rates of millimeters per year, so formation of a great mountain range requires the passage of millions of years.
U.S. Geologic Survey, "This Dynamic Earth"
University of Wisconsin, "Subduction Zones and Orogeny"
Northern Arizona University: "Hypothetical Orogeny: An Illustration of Tectonic Cycles and Mountain Building"