The reports include a progress update on the project at large and provide diagrams of many project aspects.
The reports also also take each tiny aspect of the project and provide contractor information, a description of that aspect of the project, what specifically they're doing, milestones and projected completion dates, and lots of information on costs and how they're spending the money. Each section of the report also includes a diagram and information on safety/accident rates at that particular site.
These reports contain a lot of information--pretty much every single little thing about ESA disclosed in these reports every three months. I, personally, just look through them for the pictures, but if you wanted to get a real in-depth look at exactly what's going on underground, they're worth the read.
The report for Q1 of this year will probably be available sometime in April. The complete index of quarterly reports and other reports on the ESA project is available on the MTA's website.
Here are the last four quarterly reports, for Q1 through Q4 in 2012:
