Currently there are 32 graduate employee unions in the United States according to the Coalition of Graduate Employee Unions (CGEU). They represent students across the United States, mainly in large public universities like Penn State. Of the 14 Universities within the Big Ten, 6 of them are unionized (Michigan State; Rutgers; University of Illinois at Urbana-Champaign; University of Iowa; University of Michigan; and University of Wisconsin at Madison).
This is not a static number, though. Just two years ago University of Connecticut graduate employees voted to unionize, and graduate employees are organizing at NYU, Columbia, The New School, Harvard, Yale University of Chicago, Syracuse University, and other universities.
Although each union differs according to the decisions of their members, they all operate through democratic elections to select union leadership that represents the concerns of employees. Members vote on proposals for an agreement that governs the relationship between graduate employees and the university. Then representatives of the union work toward a tentative agreement with the university. Finally, graduate employees vote to decide whether to accept or reject this agreement. University of Connecticut graduate employees just accepted their first contract, which includes a 3% yearly increase in stipends over the next 3 years; waiver of a $468 infrastructure fee, and support towards other fees; reduced costs of parking permits; reimbursement for work-related travel; and maternity (6 weeks) and paternity (3 weeks) leave.