There is a growing literature on what exactly the Quantitative Easing has achieved. As we are going see, there is an agreement that QE has led to both higher output and higher inflation, however, there is less agreement on the magnitude and persistence of these effects.
The Fed has recently announced that it will renounce to Quantitative Easing policy. Alan Blinder has a very interesting material that explains pretty well the rationales for why has the FED chosen this approach, how was implemented and what are the exit strategies.
If you read opinions like the one by James Bullard (current president of the Federal Reserve of St. Louis), you might think that Quantitative Easing has been a succes and it has shown how monetary policy can be effective even when the interest rate is near zero.
Explaining the crises (not all, but many of them) as being liquidity traps is not only a misinterpretation but it also leads to false solutions. Just look at the case of Japan after two decades of “policy experiments”. (New) Keynesians like Krugman have reduced its stagnation problem to a liquidity trap and prescribed a wrong therapy which in the end failed to lead to real economic growth. But probably the case of Japan deserves a separate discussion.
Following the effects of the last financial crisis, as the nominal interest rate hit the zero lower bound, the central banks in United States, Euro Area and United Kingdom (to be more precise, it was the Bank of Japan that experienced this approach first) have started to implement a rather extreme form of unconventional monetary policy which became known as the Quantitative Easing.