In October 2015, Albot together with his doubles partner František Čermák managed to reach the 2015 Kremlin Cup final, being defeated by Andrey Rublev and Dmitry Tursunov in the decisive set.

In June 2017, Radu Albot reached the quarterfinals of the 2017 Antalya Open beating João Sousa and Paolo Lorenzi, before losing to Andreas Seppi in straight sets.

Albot qualified for the 2017 US Open tournament and won two main draw matches before being defeated by Sam Querrey in the third round, his best singles finish at a Grand Slam to date.

In February 2018, Radu Albot reached the quarterfinals of the 2018 New York Open, winning matches against Bjorn Fratangelo and John Isner, but being eliminated by Kei Nishikori in the decisive third set.

In September 2018, he reached his first ATP Tour level singles semifinals at the 2018 Moselle Open where he lost against the eventual tournament champion, Gilles Simon.

[4][5] In late February, he won the 2019 Delray Beach Open, making history as the first Moldovan to win an ATP singles title, knocking out Ivo Karlović, Nick Kyrgios, Steve Johnson and Mackenzie McDonald.

In the final he defeated Dan Evans of Great Britain in a closely fought three-set match.

[8] In March in Miami continuing his great form, he took a set off the eventual champion Roger Federer in his second round match.

[9][10] In May, Albot reached the 2019 Geneva Open semifinal losing in the penultimate round against Nicolás Jarry.

In January 2020, Albot participated in the Inaugural 2020 ATP Cup in the Group stage as a member of the Moldovan team.

[14] Albot reached the third round at the 2021 Australian Open for the first time at this Major where he defeated World No.

[15] In February, seeded sixth, he made his first semifinal in 19 months and of the year at the 2021 Singapore Tennis Open where he lost to Alexander Bublik.

In March, he entered the main draw of the 2023 BNP Paribas Open as a lucky loser directly into the second round, replacing 15th seed Pablo Carreño Busta who withdrew in the last minute.

In May, he qualified for the 2023 French Open and won his first round match against American wildcard Patrick Kypson.

137, he qualified for the main draw at the 2024 Delray Beach Open[24][25] and won his first round match against #NextGenATP player Juncheng Shang.