Why and how will we be able to image extraterrestrial planets in the next two decades? According to a recently published article, a well-established Cambridge astrophysicist stated that:

the “origin of life, where it exists, and whether aliens exist,
  is going to be crucial over the next four decades”. He added: “We know
  now that stars are orbited by retinues of planets just as our sun is.
  We have learned this in the last decade, essentially. “Within 10 or 20
  years we will be able to image other planets like the Earth, orbiting
  other stars."

My question is, what technological limitation are we dealing with regarding making images of extraterrestrial planets, and how can this scientist be so certain that this limitation will disappear only 10 or 20 years from now?
 A: In fact, we already have imaged extraterrestrial planets. You can find a list here, with perhaps the most famous system being HR 8799.
Of course, that quote was referring to Earth-like planets, and you can see from the list I linked that everything we've seen is more massive and further out than even Jupiter. The challenge that confronts direct imaging is not so much the faintness of the planet in and of itself (large telescopes and long integration times fix that) or that planets are small (we'll only ever see a point anyway, just as for most stars in the galaxy, since the diffraction limit prevents us from resolving them without telescopes that are too large to be feasible). The problem is contrast. As mentioned in this well-known Nature paper, any Earth-like planet is sitting next to a star $10^{10}$ times brighter than it. Even without the atmosphere, any optical imperfections in your equipment in the nanometer-to-micron regime will scatter the host star's light all over your image, swamping the planet. Moreover, the noise is best handled at exposure time with the EM field phase on hand, rather than with some sort of clever post-processing of the image (which contains only intensity information).
Various adaptive optics and other techniques are being adapted for the circumstances, but I can tell you from personal experience in the field that direct imaging of an Earth-like planet will be hard. Someone might do it in the next five years, or it might take more than thirty.
A: Martin Rees is being a bit optomistic, both the Terrestrial Planet Finder and  Space Interferometry Missions were canceled because of lack of money.
A: Perhaps a more reasonable idea would be to decode signals inadvertently sent from distant planets. 
For example, if we reverse the situation then on a distant planet the ETs looking at Earth might decide it is impossible to build a telescope to see us, and instead they might start trying to understand how to decode the stray television signals we are broadcasting. If we assume the ETs have also developed a system for broadcasting images based on radio waves we should be able to do the same and see them (or at least see ET's equivalent of the X Factor).
There are drawbacks of course. Non-intelligent life will be missed, intelligent life would only be seen if a television like machine has been invented and even if ET has invented a television set it is possible the technology they use would be beyond our ability to decode. Nonetheless it might be easier than trying to build a 300 mile reflecting mirror.
