"The situation is that a man sets off in a rocket travelling at high speed away from Earth, whilst his twin brother stays on Earth. [...] ...the twin in the spaceship considers himself to be the stationary twin, and therefore as he looks back towards Earth he sees his brother ageing more slowly than himself." http://topquark.hubpages.com/hub/Twin-Paradox
David Morin, Introduction to Classical Mechanics With Problems and Solutions, Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. [...] For the entire outward and return parts of the trip, B does observe A's clock running slow..." http://www.people.fas.harvard.edu/~djmorin/chap11.pdf
Let us consider only the one-way travel (no turning around). Twin B's spaceship is so long that twin A and his clock are in the vicinity of the spaceship all along. A's clock is constantly checked against spaceship's clocks by observers on the spaceship. As stated in the quotations above, special relativity predicts that, in the spaceship system, A's clock will be found to run slower than spaceship's clocks. Accordingly, A is aging more slowly than B - a scenario is conceivable in which the spaceship stops after observers on the spaceship register that (the stationary) twin A is only 2 years older while (the traveling) twin B has aged 20 years.
Stationary (Earth's) observers will register the opposite, according to special relativity. If, when the spaceship stops, (the stationary) twin A is 20 years older, (the traveling) twin B has aged only 2 years.
Why this idiotic "theory" has been considered as the height of human wisdom for more than a century is beyond imagination.