Like many of its peers that possess modern submarines, China's submarine fleet was first stood up through the acquisition of imports but has slowly begun to include more domestic designs, especially as it has pursued the development of nuclear powered submarines. China's first submarine acquisition occurred on 4 June 1953, when China and the Soviet Union signed an accord that supplied China with 32 fully operational warships, as well as the license to build the Soviet O3-class (NATO: Whiskey) submarine.  However, it wasn't until the next year, in July 1954, that China received its first submarines from the Soviets, two S-class and two M-15 class vessels. The first Chinese-built submarine, an O3-class, was not commissioned until 1957, and not without considerable Soviet assistance in terms of parts and shipbuilding expertise. It is generally agreed that Mao Zedong was dissatisfied with Chinese reliance on Soviet assistance in building the country's submarine fleet; however, that did not prevent him from signing a second accord with the Soviet Union in October 1958, which provided Soviet designs, technical data, and equipment for the Type 33 attack submarine (NATO: Romeo) and the Type 31 ballistic missile submarine (NATO: Golf).  This assistance was crucial to China in developing its modern submarine fleet.
In total, China is known to have built over 80 Type 33 Romeo attack submarines from 1962 to 1984 as well as at least an additional 20 Type 35 Ming submarines, which were based on the Soviet Romeo design.  Given how noisy both these submarine classes were, it is not surprising that China made the decision to procure an additional 12 Russian Kilo submarines from 1994 to 2005 in addition to the diesel electric submarines that China had started developing itself in the 1980s. In December 2012, it was announced that China and Russia had signed a framework agreement for joint construction of four Project 677E Lada-class submarines.  Expected in 2015, this procurement could be very important given that the Lada is considered to be Russia's most advanced diesel electric submarine. However, the Russian announcement in early 2014 of a new Kalina-class submarine based on Air Independent Propulsion (AIP) has caused some to question whether the agreement will be revised to focus instead on this new class of submarine. 
Finally, despite the significant assistance provided by the Soviet Union for China's diesel-electric submarine fleet, the same level of assistance did not occur for China's nuclear-powered submarine fleet. There is some evidence that the Russian Rubin Design Bureau provided technical assistance for construction of the Type 093 Shang-class nuclear submarine, and it is notable that the Type 093 closely resembles the Russian Victor-III submarine.  However, it is certain that much more of the development process for China's nuclear-powered submarines was addressed domestically, which explains why Chinese nuclear powered submarines have been so slow to catch up to modern nuclear submarines technologically.
Despite China's rapid production and acquisition of submarines in recent years, it has not begun actively exporting them. It is likely that this is due to technical issues that continue to plague China's domestically built submarines. To date, the only rumored export of Chinese submarines was to Bangladesh in late 2013.  However, little concrete information exists in the open source literature to confirm this rumor. More recently, a possible deal is pending between China and Pakistan to supply Pakistan with 6 Yuan-class diesel-electric submarines.  The deal has not yet been signed, but there is speculation that it may be signed before the end of 2014.
 John Wilson Lewis and Xue Litai, "Designing" China's Strategic Seapower: The Politics of Force Modernization in the Nuclear Age, (Stanford, CA: Stanford University Press, 1994), 48.
 John Wilson Lewis and Xue Litai, "Designing" China's Strategic Seapower: The Politics of Force Modernization in the Nuclear Age, (Stanford, CA: Stanford University Press, 1994), 49.
 William S. Murray, "An Overview of the PLAN Submarine Force" China's Future Nuclear Submarine Force, (Annapolis Maryland: Naval Institute Press, 2007), 60.
 "Jane's World Navies - China," IHS Jane's, 13 March 2014, www.janes.com.
 Zachary Keck, "Russian may sell China new Advanced Submarines" The Diplomat, 28 March 2014, www.thediplomat.com.
 Shawn Cappellano-Sarver, "Naval Implications of China's Nuclear Power Development," China's Future Nuclear Submarine Force, (Annapolis Maryland: Naval Institute Press, 2007), 125-126.
 "Bangladesh Finalizes 2 Type 035 Ming Class submarine deals with Beijing" Asian Defense News, 31 December 2013, www.asiandefensenews.com.
 Farhan Bokhari, "China, Pakistan set for submarine deal by end of year, say officials," IHS Jane's Defense Weekly, 2 February 2014, www.janes.com.