On 1 September 2015, Glover starting playing Fantine in the second Broadway revival of Les Misérables, she left the production on 3 February 2016.[2]
From 9 September 2017 to 31 March 31 2019, Glover portrayed Angelica Schuyler in the Chicago cast of the Broadway blockbuster Hamilton.[3]
On 6 September 6 2022, she started sharing the role of the Witch with Patina Miller in the 2022 Broadway revival of Into the Woods.[4] She left the production on 15 December 2022 being replaced by Joaquina Kalukango.[5] She reprised her role in the 2023 national tour.[6]
She has performed on Broadway in the musical Memphis as Felicia. Glover received a nomination for the Tony Award for Best Performance by a Leading Actress in a Musical for her performance. Additionally, she won the Drama Desk Award for Outstanding Actress in a Musical (in a tie with Catherine Zeta-Jones).[9] She displays a "rich, rangy and emotionally powerful voice in several standout numbers" according to Playbill.[10] Montego has been with Memphis since it started, including four regional productions[11] and appears in the live filming of the musical, Memphis: Direct from Broadway.
Her Broadway debut was as an understudy for Celie and Nettie in the musical The Color Purple.