In the end,Everyone discovers that light is kira because of a simple mistake he had made.Matsuda shoots light in the arm and then light runs out the door and keeps running till he reaches a building,he limps up the stairs,right as he goes up,ryuk(shinigami) writes down light's name in his deathnote and light dies within a matter of seconds.

In the end, everyone discovered that Light is Kira and then he got killed by Ryuk based on their agreement.