In 1905 Einstein derived, from his two postulates, the conclusion
"the clock moved from A to B lags behind the other which has remained at B":
Albert Einstein, On the electrodynamics of moving bodies, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B." http://www.fourmilab.ch/etexts/einstein/specrel/www/
This conclusion does not follow from Einstein's 1905 postulates - the argument is invalid. The following two conclusions, in contrast, VALIDLY follow from the postulates:
Conclusion 1: The clock moved from A to B lags behind the other which has remained at B, as judged from the stationary system.
Conclusion 2: The clock which has remained at B lags behind the clock moved from A to B, as judged from the moving system.
Conclusions 1 and 2 (symmetrical time dilation) in their combination give no prediction for the readings of the two clocks as they meet at B.
In contrast, the invalidly deduced conclusion ("the clock moved from A to B lags behind the other which has remained at B") provides a straightforward prediction - the moving clock is slow, the stationary one is FAST (asymmetrical time dilation). The famous "travel into the future" is a direct implication - the slowness of the moving clock means that its (moving) owner can remain virtually unchanged while sixty million years are passing for the stationary system:
Thibault Damour: "The paradigm of the special relativistic upheaval of the usual concept of time is the twin paradox. Let us emphasize that this striking example of time dilation proves that time travel (towards the future) is possible. As a gedanken experiment (if we neglect practicalities such as the technology needed for reaching velocities comparable to the velocity of light, the cost of the fuel and the capacity of the traveller to sustain high accelerations), it shows that a sentient being can jump, "within a minute" (of his experienced time) arbitrarily far in the future, say sixty million years ahead, and see, and be part of, what (will) happen then on Earth. This is a clear way of realizing that the future "already exists" (as we can experience it "in a minute")." http://www.bourbaphy.fr/damourtemps.pdf
Conclusion: If logical validity is obeyed, special relativity is unable to say which clock - the moving or the stationary - lags behind the other. Einstein's invalid argument masks this inability and does say how the two clocks differ but this is not science of course.