Here are two recent resources on the use of the Old Testament in the New Testament.
First, a shorter one: This article by Michael Vlach is one of the most helpful summaries and interactions I have seen. It is a short (fifteen pages) and accessible work that outlines various approaches. It does not attempt to resolve the issues, but rather to lay out the positions and show some questions that should be asked of each position.
Vlach’s article is excellent for those relatively new to the discussion. But I think it would also be beneficial for those familiar with the topic. Vlach’s strength is his simplicity and clarity (something we could all stand a bit of).
Second, a longer one: Greg Beale’s Handbook on the New Testament Use of the Old Testament: Exegesis and Interpretation (Kindle edition) is a new work, but is imminently readable and understandable. At a few points, Beale tends to be repetitive (though not identical which can cause some confusion). But overall, this is a very helpful work. At 192 pages, it is not intimidating, but it is also not simplistic.
Reading Vlach’s article as an introduction to anything else on this topic would undoubtedly be helpful.