Nicely written summary on algorithmic randomness.
I have made a number of small changes/corrections to typos, directly in the article.
I have only one comment: In the section "The computational power of randomness" it is mentioned that K-trivial sequences solve Posts problem. This is actually also true for the earlier low for random sets in KuceraTerwijn. (Downey et al. made this even more simple by showing that the construction can be made priority free.)
It is useful (and logical) to give a precise reference for each "Name (Year)" in the text
Comments on review
I edited the section on Post problem.
Regarding the references, I, too, think this would be logical and useful, but the guidelines suggest keeping the references to a minimum, giving only books and major survey articles.