He was a member of the Children's Drama Group of the Serbian Radio and television, and he began his acting career at the Youth Atelier in Pančevo.

In 1996, he received a scholarship from the Yugoslav Drama Theater and a role in the play The Great Robbery, directed by Dejan Mijač on the stage of Atelje 212.

[3] He played the main roles in the films Premeditated murder, Cabaret Balkan, Sky Hook, When I Grow Up, I'll Be a Kangaroo, Klopka, Hadersfild, The Woman with a Broken Nose, The Man Who Defended Gavrilo Princip, Circles, Ravna Gora and the Constitution.

[4] He moved with his family from Trebinje to Opovo in 1974, and a year and a half later to Pančevo, where Nebojsa's father was ordained a priest in the Church of the Assumption.

After two years of studies, he changed his mind and in 1990 he enrolled in acting at the Belgrade Faculty of Dramatic Arts in the class of Professor Vladimir Jevtović.

[14] Nataša Ninković, Nela Mihailović, Daniela Kuzmanović, Danijela Ugrenović, Karolina Cimeša, Vojin Ćetković, Sergej Trifunović and Boris Pingović studied together with Glogovac.

[22] In addition to acting he was a passionate lover of horseback riding, dogs, backgammon, cars and motorcycles, he loved cooking, and in his childhood he practiced handball.

[29] Glogovac was the official promoter of the derby match of the 8th round of the Serbian Super League playoffs in handball between Partizan and Crvena Zvezda, which was played in March 2014, and was of a humanitarian nature, to help those threatened by floods in Serbia in 2014.

The following year, he cut a lock of his hair as a sign of support for children suffering from cancer and their parents, as part of the Strand of Hope campaign.

[42] It is represented in the 2018 books Untold Stories by Croatian director Rajko Grlić and Ne damo svetinje by Serbian poet Slavko Perošević.

During his early childhood, he spent time in the family house of his grandfather Gavrilo and grandmother Darinka in the mountain village of Dramiševo, not far from Nevesinje.

[55] From 1997 until 2014, Nebojša was married to Mina Glogovac, a painter and assistant professor in the subject of Painting Techniques at the Faculty of Applied Arts in Belgrade.

[58][59] Two years after the divorce, Glogovac had a third child, a daughter named Sunčica, with his wife Milica Šćepanović, a yoga instructor, and former journalist.

[15][66] In his second year at the Faculty of Dramatic Arts in Belgrade, he got a role in the play "The Great Robbery," directed by Dejan Mijač, on the stage of the Atelje 212 theater, which premiered on 9 August 1992.

[67] He made his debut at the Yugoslav Drama Theatre in the play "False Emperor Šćepan Mali," in the role of Niko Đurov, on 24 July 1993.

[71][72] In the drama "Raj (Heaven)" directed by Petar Zec, which premiered in 1993, he was one of the main actors, in the role of Birimić, a friend of Miloš Crnjanski, played by Tihomir Stanić.

[74][75][76] In 1994, he got the role of Fadil, a JNA soldier, in Boro Drašković's war drama "Vukovar, jedna priča"[77] After drawing attention to his talent, he got a role in the film directed by Gorčin Stojanović, "Premeditated Murder" (1995), in which he played the character of Bogdan, wounded in the Bosnian War, who is impatiently waiting for his recovery to return.

In the same year, he played one of the main roles in the movie "Savior," where he portrayed Vera's brother, a raped Serbian woman who spent the war in a prison camp.

This was followed by the role of the main character, Marko, in the film "Ranjena zemlja," which takes place in a Belgrade shelter during the NATO bombing of the FRY.

[82][83][84] Based on a months-long survey, the daily newspaper Večernje Novosti compiled a list of the best actors and actresses in Serbia in 2000, and Glogovac took the 50th place.

[90][40] In the crime thriller "Klopka" (2007), Glogovac got the main role as Mladen, a construction engineer who tries in every way to earn money to cure his seriously ill son.

[91] In the film drama "Hadersfild," he played the role of Ivan, a former Judoist who went through a series of psychotic episodes and treatment in mental institutions before finally being baptized in the Eastern Orthodox Church.

[100][101] In March 2012, together with Bojana Ordinačev, Vuk Kostić, Viktor Savić, and Nataša Ninković, he was a member of the jury of the J Factory film competition.

[107] Collaborating with Katarina Gojković, Nikola Vuković, and Anja Knežević, he recorded the children's song "Moj ujak i ja(My uncle and I)," included in the 2014 music album Dečje zavrzlame i ostale kerefeke za mame, tate, bake i deke (Children's tangles and other kerefeks for mothers, fathers, grandmothers and grandfathers) by Radivoj Radivojević.

[94] In Srđan Koljević's film "The Man Who Defended Gavrilo Princip" (2014), Glogovac played Leo Pfeffer, reprising the role in the 2015 series of the same name.

[110] He also played a significant role in Radoš Bajić's film "Za kralja i otadžbinu (For the king and the country)" (2015), portraying Dragoljub Mihailović for the second time in his career.

[112] After a short but severe battle with lung cancer, Glogovac died at the age of 48, on 9 February 2018, in Belgrade's Institute for Oncology and Radiology of Serbia.