This is such an important issue that it bears repeating. I've updated some charts to make my point clear.
As the chart above shows, the Chinese yuan has been rising against the dollar ever since 1994. The Chinese are demonstrably not undervaluing their currency, they are continuous revaluing it. They have been forced to do this because of the tremendous inflow of capital to the country, which in turn has been driven by the world's desire to invest in this rapidly growing and dynamic economy. Since China's monetary policy is geared towards pegging its currency against the dollar, a net inflow of dollars and other currencies to the country obliges the central bank to buy the extra currency, thus adding to its forex reserves and expanding its monetary base. This is the way that capital inflows get turned into yuan and help the economy grow. But as the chart also shows, forex reserves swelled to over $3 trillion by last year, way more than enough to credibly back China's currency and its money supply.
For the past year, there has been no net addition to China's reserves, which means that there is no longer a net inflow of capital to China. This could be one sign that the currency is properly valued, and/or it could be a sign of a diminished desire on the part of foreigners to invest in China, and/or diminished investment opportunities in China, and/or a greater desire on the part of Chinese to invest abroad. Whatever the case, the central bank is no longer buying foreign currency to keep the yuan from rising, but they are still allowing the yuan to appreciate. This is not the behavior you would expect from a currency manipulator. If anything, the Chinese seem to be "manipulating" their currency higher against the dollar, not lower. And they might be doing this in order to proactively deflect criticism from misinformed and misguided politicians in the US.
This next chart shows the real value of the yuan against a large basket of currencies, as calculated by the BIS. Since it was first pegged to the dollar in 1994, the yuan has appreciated in real terms by 64%! Even supposing the yuan was purposefully undervalued in 1994, it is hard to believe that it is still undervalued today.
By pegging the yuan to the dollar, China effectively outsourced its monetary policy to the Federal Reserve. On the surface, both countries have the same monetary policy, so both should have the same inflation rate, and that is indeed what has happened, as the chart above shows. China has been living under a US-influenced monetary regime for almost 20 years now, and its economy has had plenty of time to adjust. If the yuan were still undervalued, as Romney and even Obama claim, then Chinese inflation should be higher than US inflation, but it's not.
Anecdotal evidence suggests that on the margin more companies are finding it cheaper to produce goods in the US than in China, and that's part of the reason for the stability of China's reserves over the past year. It all adds up to evidence of a sort of equilibrium having been attained between the value of the yuan, the relative price levels in China and the US. The yuan has successfully compensated for the different level of productivity and specialization in each country.
There is nothing here to worry about, with one big exception: if the US tries to start a trade war with China to force it to revalue its currency even more, then we are all going to be in big trouble. The US could suffer from rising inflation (demanding a stronger yuan is equivalent to wanting a weaker dollar), while the Chinese could suffer from deflation. It's the politicians, not the Chinese, that pose the biggest threat to the US economy.