Controller
A Controller or Gamepad (aka Game Pad) is an input device commonly associated with Consoles, although many PC games support controllers as well.
History
When Tomb Raider and its successors up until The Last Revelation first appeared, they was released for most of the 5th generation consoles like the original PlayStation or the Dreamcast. The main method of input on these consoles were analog or digital gamepads that featured four directional buttons and four action buttons (like the iconic and trademarked 
, 
, 
, and 
on the PS) along with some additional buttons like "Start" and "Select" and shoulder buttons. On analog 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 manly supported old style Gameport Joysticks, along them Tomb Raider. There were also some gamepads for this interface.
By the end of the 1990s these original gamepads - a legacy from even earlier console generations - 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 deprecated interfaces to USB. These controllers mostly work with PCs, too, as long as the correct Windows drivers are installed. Some older controllers like the DualShock 2 of the PS2 can still be used by means of an USB adapter.
Today 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 contoller. 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.
