What are the MBA application deadlines for summer internships?
Most firms will start having networking events and info sessions on campus in the fall to meet first year MBA students before they apply for the summer internship (between yr. 1 and 2 of MBA).
Application deadlines vary by school, but they are typically in November or December for MBA students.
From there, interviews are typically in January-February. Some firms (MBB and a few others) allow PhD students to apply for this internship as well and timing is similar.
For 2020-21 deadlines, see this page.