There are two disputes over Kashmir or parts of it.

The less scary one is between China and India over parts of the state of Jammu and Kashmir. This dispute does not include the Kashmir valley itself. I dont know the exact details of the Chinese but they derive from agreements between the British and Tibet. I will leave this dispute for someone more knowledgeable to explain.

The more scary dispute is between India and Pakistan over the entire state of Jammu and Kashmir. I will divide the history of the dispute into four phases. I am an Indian and can only talk about the Indian narrative.

1. Independence/Parition - When the British granted independence to India and Pakistan, the the hundreds of pricely states were given the choice to either join India or Pakistan. Mountbatten the last Viceroy of India had told hte princely states to choose based on the will of the people who inhabited the states. As of 15 august 1947, almost all the states that were to join India had agreed to do so. There were three states that had held out. These were Junagadh, Hyderabad and Jammu and Kashmir. The former two had muslim rulers with hindu populations and J&K had a hindu ruler with muslim population. The ruler of J&K, tried to play India and Pakistan against each other to ensure that he coud rule over an independent state. However soon after independence, tribal militias (kabalis) invaded from the west and quickly overran much of his army, half of which defected to them. These militias are believed to have been supported by Pakistan, where they are referred to as freedom fighters fighting against the tyranny of the king. The king then asked for help from India, but was told that no help would be provided unless he joined India. He agreed. Indian troops were sent to J&K and were able to push back the irregulars to the extent that is now controlled by India. At that point the Pakistani army openly entered the conflict and the situation came to a stalemate. These were two armies that had been a single entity till very recently and had identical training and equipment.

The matter was referred to the UN where the resolution called for a plebiscide to be held. This could not be done as India demanded that the irregulars that had captured the territories withdraw. Since neither side trusted the other to not take advantage of the withdrawal, no such plebiscide took place. A good summary of the points held by either side with regards to the UN resolution is present in the history section of this wiki page : http://en.wikipedia.org/wiki/Jammu_and_kashmir

2. Upto the start of the insugency - in 1952 a constituent assembly that was formed in the Indian part of J&K which agreed to ascede to India. The region was mostly peaceful with trade and tourism flourishing. India and Pakistan however continued their animosity and could not come to an agreement acceptable to either side. They fought two wars, one in 1965, over Kashmir which ended as a draw and one in 1971 over Bangladesh, which created Bangladesh. The situation in J&K remained tense at the borders all through. Once significant instance was the skirmish over the Siachen Glacier http://en.wikipedia.org/wiki/Siachen_glacier

3. Insurgency, Kargil and Afghanistan - Democratic development was limited in Kashmir until the late 1970s and by 1988 many of the democratic reforms provided by the Indian Government had been reversed and non-violent channels for expressing discontent were limited and caused a dramatic increase in support for insurgents advocating violent secession from India. In 1987, a disputed State election created a catalyst for the insurgency when it resulted in some of the state's legislative assembly members forming armed insurgent groups. These groups were actively funded, armed, and trained by Pakistan. This led to worseing of relations between India and Pakistan. India used a very heavy handed approach to stamp out this insurgency which turned many more people against it and several accusations of human rights violations cropping up. These accusations would then be used by Pakistan and the insurgents to further stir up support against India. The peak and end of this phase will break the 20 year rule so I will not talk about them. One of the narratives (huge Indian bias here) is that Pakistan had gained a lot of expertise in supporting insurgencies by supporting the mujahedeen in Afghanistan against the USSR. Once the soviets withdrew from Afghanistan, this infrastructure was turned to forment trouble in J&K and the insurgency would have taken place even without the trigger of allegedly rigged elections.

The above gives us some context about what was hppening in Kashmir and why its disputed. However it does not explain why it is so highly contested, much unlike the dispute between India and China. I shall present two arguments here plus a tinoily one.

1. Water - The Indus flows through J&K, as do several of its tributaries like the Sutlej. These rivers form the majority of freshwater available to Pakistan. It therefore becomes extremely important for Pakistan to maintain control of J&K so that India does not at some point block off hte flow of water, or divert it.

2. Ego - yes ego, and yes it sounds stupid. J&K has become a point of ego for both the countries, neither country is willing to back down from its position and look weak to the 'enemy' country. This enemity has been around since partition and the kashmir dispute is a consequence of it, not a cause.

3. Ideology behind partition - This is a very tenuous and borderline tinfoil theory. According to this theory, India has held itself to be a secular state and not a hindu state as Pakistan claims, hence to prove itse secularity, it has to keep Kashmir, the only muslim majority state in India. As a mirror image o the paksitani side, Pakistan was created to protect muslims of the indian subcontinent from the tyranny of the hindu majority. A prosperous muslim majority state in India undercuts the argument for the existence of Pakistan and therefore Pakistan has to have Kashmir.