What's relation between Kolmogorov complexity and pseudorandomness?

Question

In a comment on this question, @Kaveh wondered whether the questioner really wanted to ask "is there a relation between strings with high Kolmogorov complexity and pseudorandomness?" This is not the question that was answered, in the end, but I would like to know the answer.

I understand that any pseudorandom sequence can be given a short description, by describing the program that generated it (as Travis M. points out in the question linked above). So in one sense the sequence such a sequence does not have high Kolmogorov complexity.

On the other hand, it seems as if there's some connection between pseudorandomness and Kolmogorov complexity. For if you didn't know the algorithm, then sequences generated by a good (passes lots of appropriate statistical tests, etc.) PRNG could not be described more briefly than by giving the sequence--on average, at least. Right? That's implicit in the kind of tests that good PRNGs have to pass: The tests are meant to rule out cycles and other regular patterns. (We can also require that the PRNG be cryptographically secure, if that helps.)

Happy to be told that I'm hopelessly confused. Just point me in the right direction.