Notable members of the club include Šarūnas Marčiulionis, Šarūnas Jasikevičius, Ramūnas Šiškauskas, Arvydas Macijauskas, Jonas Valančiūnas, Martynas Gecevičius, Renaldas Seibutis, Simas Jasaitis, Robertas Javtokas, Darius Songaila, Marijonas Petravičius, Rimantas Kaukėnas, Rimas Kurtinaitis, Gintaras Einikis, Deividas Sirvydis, Rokas Giedraitis, Artūras Gudaitis, Ąžuolas Tubelis.

[4] Jonas Kazlauskas, Rimas Girskis, and then-head coach Rimantas Endrijaitis led Statyba to third place in the 1979 Soviet Union Championship.

In 2000, Ramūnas Šiškauskas, Andrius Giedraitis and Eric Elliott, combined with Arvydas Macijauskas and Robertas Javtokas, managed to win LKL.

Tyrone Nesby, Roberts Štelmahers and Robertas Javtokas, Simas Jasaitis and Tomas Delininkaitis led the team to victory in the 2005 ULEB Cup, beating Pamesa Valencia in the semifinals and Makedonikos in the final.

Those wins allowed Rytas to advance to the Top 16 phase, where they won three times out of six, beating Tau Ceramica Vitoria once and Brose Baskets Bamberg twice.

Although the coach and three leading players Robertas Javtokas, Simas Jasaitis and Fred House had left the team during the interseason, the 2006–07 ULEB Cup season was rather successful for Lietuvos rytas.

NBA player Kareem Rush arrived to lead the team to the ULEB Cup final where Real Madrid defeated Lietuvos rytas.

However, Real Madrid's victory at the ACB semifinals, and of one of four spots reserved for Spain, allowed Lietuvos rytas to take part in the 2007–08 EuroLeague as the ULEB Cup finalist.

During the 2008–09 season, Lietuvos rytas, affected by the worldwide financial crisis, had a significantly lower budget and put a greater emphasis on prospective local players.

After an unsuccessful start of the 2010–11 EuroLeague, Dražen Anzulović was replaced by the team's former coach Aleksandar Trifunović, then Šarūnas Jasikevičius, and finally Simas Jasaitis.

[13] Playing in the Group E in EuroLeague, Lietuvos rytas defeated Caja Laboral at home, Panathinaikos Athens and Unicaja Málaga on the road, finishing ninth, the highest achievement for the team in this tournament in club history.

In EuroLeague's qualification tournament, which was organized in Vilnius, Lietuvos rytas won their first two matches against Budućnost Podgorica and Cibona Zagreb, but lost the final game against Galatasaray.

Former team leader Martynas Gecevičius was recalled after a two-season break and point guard Omar Cook was signed[16] alongside Darius Songaila.

[20] After being eliminated in the EuroCup playoffs by Crvena zvezda Belgrade, Lietuvos rytas also suffered a defeat in the LKF Cup finals - losing to TonyBet Prienai 92–91.

After defeating Lietkabelis Panevėžys in the quarterfinals 88–82, Neptūnas Klaipėda in the semifinals 97–79, and Žalgiris Kaunas in the final 67–57, the team won their first trophy following a five-season drought.

[48] On 19 June 2017, famous poker player, businessman and European Parliament member Antanas Guoga bought fifty percent of the club from Sigitas Židonis and Remigijus Kazilionis.

[58][59] Guoga also told the media it was very likely that at least two Lithuanian basketball stars will participate on the team, in addition to Jonas Valančiūnas, Linas Kleiza and Arvydas Macijauskas.

[65] Despite positive changes in the club, rifts between the new owners started to emerge after it announced a sponsorship agreement with Lithuanian business consortium MG Baltic.

These changes helped, as Rytas won the most important game in the regular season, by defeating Alba Berlin 94–73 and avenging their first round loss.

In the final home game in the EuroCup, Rytas lost to Bayern Munich 87–85, another poor defensive showing, and finished with a 1–5 record and last place in Top 16 group F.[86] "I want to underline that this team is special.

Rytas also signed point guard Matt Farrell, scoring leader from the University of Notre Dame, but he was released just before the season for reported personal reasons.

Due to the COVID-19 pandemic, the LKL season ended prematurely - Žalgiris were announced as the winners, while Rytas finished second - one win over third-placed Lietkabelis Panevėžys.

[15] In the 2019–20 EuroCup Basketball season, Rytas played in Group B, with Umana Reyer Venezia, Partizan NIS, Tofaş, Lokomotiv Kuban and Limoges CSP.

[92] Therefore, the club decided to choose the Basketball Champions League instead of the EuroCup due to a much more beneficial financial offer and returned to a FIBA competition for the first time since the 2002–03 season.

Also, Rytas signed with a former EuroLeague star Andrew Goudelock, Demetrius Jackson, who proved to be a pleasant surprise, Chris McCullough, and Lithuanians Saulius Kulvietis, Rokas Gustys, Gytis Radzevičius, Lukas Uleckas, Augustas Marčiulionis.

High hopes, nonetheless, once again hit some road blocks by January–March - the win streak ended with a close home loss to Žalgiris, who took first place in the LKL regular season, and Rytas struggled in the Champions League Round of 16 stage, falling behind Lenovo Tenerife, and SIG Strasbourg, finishing just out of the playoffs due to a point difference with SIG Strasbourg.

In a much hyped game in Panevėžys, facing a deficit, Rytas managed to pull a win over Lietkabelis 78–77, on a dunk in the deciding seconds from Butkevičius, and took a 3–1 lead in the LKL finals.

Benedek Váradi and former LKL MVP with BC Šiauliai Elvar Már Friðriksson were signed as the new point guards to replace Kariniauskas and Smith.

Rytas lost to Nevėžis-OPTIBET in King Mindaugas Cup qualifiers in their first game, 78–70, having to win at least by nine points their second match in Vilnius to advance to the Final Four tournament, held in Šiauliai.

Rytas also signed new point guards Arnas Velička and R.J. Cole, center Javin DeLaurier and power forward Oskaras Pleikys to contracts.