"India is now a nuclear weapons state. We have the capacity for a big bomb now. Ours will never be weapons of aggression." - Indian Prime Minister A. B. Vajpayee. 
|Fig. 1: Map of the world showing non-signaturies of the NPT in red. (Source: Wikimedia Commons)|
The United Nations Office for Disarmament Affairs opened the Non Proliferation Treaty (NPT) in 1968 and it entered into force in 1970. The purpose of the NPT is to prevent the spread of nuclear weapons and weapons technology and promoting the uses of nuclear cultivation towards beneficial causes such as nuclear energy.
With regards to member nations, a total of 190 states have joined the Treaty. (See Fig. 1.) North Korea joined in 1985 but announced its withdrawal in 2003. Of the member UN states, India, Israel, Pakistan and South Sudan have chosen to not sign the NPT. Of them, all but Israel are transparent about the possession and development of nuclear weapons.
Being the non-signers of the NPT, several trade sanctions were imposed on India, straining several international relations. One of the biggest reasons for India to join the NPT was the access to "peaceful nuclear technology" from the nuclear countries to the non-nuclear countries so the latter could develop their programs. The restricted international trade prevented India from obtaining nuclear resources to develop their nuclear program, leading to a temporary dead end.
India wishes to be on a member of the UNSC (United Nations Security Council). All the members of the UNSC are members of the NPT, it is speculated that this might be the source of some friction for India.
The spirit of the NPT creates a divide, between countries that did develop nuclear power before 1967 and those that didn't develop nuclear power before 1967. It only gives the 'Permanent 5' the right to hold weapons. Although it permits the use of nuclear energy for constructive purposes, it puts all the other nations at risk.
India, despite being a nuclear weapons state, would have had to sign the treaty as a non nuclear weapons state, and in addition has to undergo inspections.  The NPT, in India's opinion doesn't explain the need for this distinction and loss of national sovreignity.
India did however; sign the "no first use" treaty (which later changed to the no first use against non-nuclear weapon states) in 2010. 
In a Joint Statement Between President George W. Bush and Prime Minister Manmohan Singh in October 2008, the two countries signed the nuclear 123 deal which in essence separates India's civil and military facilities and place all its civil facilities under International Atomic Energy Agency (IAEA) safeguards. [4,5] This gave India complete power to stay out of the NPT, keep our weapons, not be subject by checks, and undergo full nuclear trade. 
© Surya Narayanan. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 K. J. Cooper, "Premier Says India Capable of 'Big Bomb'," Washington Post, 16 May 98.
 "Treaty on the Non-Proliferation of Nuclear Weapons," International Atomic Energy Agency, Information Circular INFCIRC/140, 22 Apr 70.
 L. Weiss, "India and the NPT," Strategic Analysis 34, 255 (2010).
 M. Sultan and M. B. Adil, "The Henry J. Hyde Act and 123 Agreement: An Assessment," South Asian Strategic Stability Institute, SASSI Policy Brief 11, September 2008.
 "Joint Statement Between President George W. Bush and Prime Minister Manmohan Singh," Public Papers of the Presidents of the United States: George W. Bush, Book II, 2005 (U.S. Government Printing Office, 2011), p. 1236.