China and India have a number of border disputes with one another. For a very good graphic look at all of the disputes between the two countries, please follow this link.
The problems between India and China relate to the difficulty of the terrain and the legacy of English colonization. Britain did not define the boundaries of India in any very precise way when it had control of India. There was a great deal of room for error in the border it drew and it never bothered to be more specific. When India gained independence, then, its borders were unclear. Then both China and India took various actions that caused tensions to arise. For example, China took Tibet, which increased the length of its border with India. At the same time, Indian troops moved into an area called Tawang that China claims is part of Tibet.
Because the two countries have such a long border through mountainous terrain, and because the border was never well defined, there are border disputes between them.