When Tomb Raider and its successors up until The Last Revelation first appeared, they were released for most of the 5th generation gaming consoles like the original PlayStation or the Dreamcast. The main method of input on these consoles was analogue or digital gamepads that featured four directional buttons and four action buttons (like the iconic and trademarked , , , and on the PlayStation) - along with some additional buttons like "Start", "Select", and shoulder buttons. On analogue gamepads at least the directional buttons can transmit analogue values, e.g. not only "pressed" and "released" signals, but also something like "half pressed".
At that time PC games mainly supported old style Gameport Joysticks, along them Tomb Raider. There were also some gamepads for this interface, but the number of supported buttons and sticks was limited by the interfaces specification.
By the end of the 1990s the original legacy 5th generation console gamepads were enhanced with Analogue Sticks, small joysticks that can be manipulated with the thumbs, and even rumble capabilities (aka Force Feedback or DualShock) were added. Most manufacturers switched from proprietary (or by then deprecated) interfaces to USB. These controllers mostly work with PCs, too, as long as the correct Windows Device Drivers are installed. Some older controllers like the DualShock 2 of the PlayStation 2 can still be used by means of an USB adapter.
Today (since 2015) console controllers contain additional features like audio input/output capabilities for chats or touch sensitive buttons or even small TFT touch screens like the Wii U controller. The PlayStation 4 even supports the Vita as an controller-like input device via Remote Play. As a means of connection most manufactures have moved to wireless protocols like Bluetooth.
On PCs nowadays many gamers use the Xbox 360 controllers as they are supported by most newer games via Xinput, but other gamepads are common, too. Still, there are many players who prefer a keyboard/mouse input as it permits faster reaction times.
Gamepads and Tomb Raider
As the Tomb Raider Games were at first primarily targeted at gaming consoles, all of them support gamepads even on PC hardware, as do the Lara Croft Games. The classic games up until Tomb Raider V use the D-Pad of the controller, later games used the analogue sticks for moving Lara (left stick) and the camera (right stick).