Graduate students at private universities were recognized as employees by the NLRB this past August. The key word here is "employees", as this distinction is what provides graduate students with the right to unionize. For some context, it’s important to note that graduate students at public universities have had this status for a long time. Here is an article that sums up the decision, and the context of the case.
Other important resources are two amicus briefs, which are court documents filed by non-litigants with the purpose of providing relevant information that should be considered. One of these briefs was filed by the AAUP (the Wikipedia page has a lot of good information on the AAUP). The AAUP is an organization of roughly 47,000 professors dedicated to promoting academic freedom and shared governance. The other brief was filed by a group of private universities, and makes many arguments that we feel are at best supported by inconclusive evidence. The NLRB shared this sentiment, and in their decision, they describe how many of these arguments are "unsupported by legal authority, by empirical evidence or by the board's actual experience."
It's very telling that the brief in favor of graduate student unionization came from a large, prestigious organization of professors (this organization is over 100 years old, and has had notable members including Albert Einstein and John Dewey), while the brief against graduate student unionization came from a collection of prestigious private universities. This demonstrates a rift in opinions regarding this matter between professors and high level administrators. The brief filed by the AAUP cites the following 3 studies, here, here, and here (unfortunately the last 2 are behind paywalls), to demonstrate that "Unionization of Graduate Student Assistants Does Not Harm Faculty-Student Mentoring Relationships In Any Academic Discipline."