Theory and Applications of Categories (or just TAC) is an online journal about category theory. In addition to new material, they also make available important classics that have been hard to find.
The website is http://www.tac.mta.ca/tac/, from which you have access to all articles in all issues. Note that http://www.tac.mta.ca/ does not work.
Controversies: TAC is a high-quality journal with an impressive editorial board, but unfortunately it is not listed on commercial lists of prestigious journals like the “Science Citation Index” and “Current Contents”; we should fight to improve this. Unfortunately, also the citations from TAC are not yet counted on MathSciNet either, due to the unpopularity of category theory in the leadership of the AMS.
Urs Schreiber: Lately I have been wondering what will be happening to this unpopularity of category theory among AMS in light of recent developments. Before long and opposing category theory in math will be a bit like opposing the use of complex numbers (there was a time when that was vehemently opposed by some, too) and currently the impetus of this development comes notably from US researches, and there notably from AMS grantees.
Zoran Škoda: I recall from 1990s that the whole Grothendieck school was at that time very unpopular in US, and recall mean jokes about Grothendieck (like “the French mathematician whose only example of a big theory was a circle”) and even recall being scorned by an algebraist because of using schemes in a discussion; the popularity of stacks (and similar notions) in recent mathematical physics changed the balance in the geometric part of the story since then. But I am not optimistic that so soon we could see more general change beyond central parts of pure mathematics and formal mathematical physics. I mean, we do see the huge coming influence of category theory in central parts of pure mathematics (algebra, topology, modern geometry), but not much in most of analysis, including so popular PDEs as well as in stochastics and probability; then influence in one direction of mathematical physics, but I would not say in mainstream theoretical physics (to name few major areas say highTc superconductivity, perturbative analysis of standard model and its extensions, turbulence theory, plasma physics and so on) either. Combinatorics is in between, it is huge area where most often deep knowledge of categories will not help radically, but there are so many examples of wonderful cooperation. We should keep in mind that modern geometry, algebra and topology while so central to us they are not nearly a half of an average department in math, the rest being mathematical biology, financial math, PDEs, ODEs, probability, algorithms, complexity theory, operator spaces, metric geometry, complex systems, game theory and so on…