The company has three divisions, reflecting its ownership stakes in the Formula One Group, Sirius XM, and Live Nation Entertainment.

As of 2024,[update] Liberty Media is set to own three global motorsport businesses in the form of Formula One, Grand Prix motorcycle racing and World Superbikes.

AT&T bought the other TCI businesses—@Home Corp., National Digital Television Center and Western Tele-Communications Inc.—for $2.5 billion in cash.

[21] On September 10, 1999, Liberty Media Group renamed TCI Music to Liberty Digital Inc. (NASDAQ symbol: LDIG), with the new company trading on NASDAQ's National Market tier, after Liberty Media traded most of its Internet content, interactive television assets, and rights to provide AT&T's cable systems with interactive services, in addition to cash and notes valued at $150 million, for TCI Music stock.

Liberty Media President and CEO Robert R. Bennett said the deal would benefit stockholders of both companies.

[26] Liberty Media's Discovery Channel and QVC continued to do well, but the newer projects had problems and the company's stock price dropped by half.

[28] This was one of three possible actions to ensure federal approval of AT&T's $54 billion acquisition of MediaOne Group—the others were selling its 25.5% share of Time Warner Entertainment and dropping 11.8 million cable customers.

[31][32] In June 2002, Liberty Media acquired Wink Communications, a maker of set-top boxes founded by Brian P. Dougherty (of GEOS fame), for $100 million.

For example, it was the largest shareholder in News Corporation (though the founding Murdoch family owns more voting shares), and had a 4% stake in Time Warner.

[35][36] Liberty negotiated an asset swap with News Corp. and Time Warner that would give it control of DirecTV and the Atlanta Braves baseball team.

[37] On February 12, 2007, the deal was completed with Time Warner wherein Liberty would receive the Atlanta Braves and a group of craft magazines, along with $1 billion in cash in exchange for 60 million shares of Time Warner stock (valued at $1.27 billion as of market close on February 12, 2007).

[39] On February 20, 2008, the Federal Communications Commission approved the exchange of 16.3% of News Corp. for 38.4% of DirecTV, an $11 billion deal that also gave Liberty sports networks in Denver, Pittsburgh and Seattle plus $550 million in cash.

[41] Liberty announced plans in April 2011 to sell WFRV and WJMN to Nexstar Broadcasting Group for $20 million.

[62] Liberty Media acquired ticket distributor and hospitality group QuintEvents for $313 million in September 2023.

[64] On April 1, 2024, Liberty Media announced its planned acquisition of 86% of Dorna Sports, which own MotoGP and WSBK.

GCI is a corporate sponsor of the Iditarod, an Alaskan dogsledding race that has lost multiple participants and sponsorships over the years.

[74] More than a dozen companies, including ExxonMobil, Alaska Airlines, and Chrysler, have dropped their Iditarod sponsorships over the years, amidst campaign efforts from PETA showing the conditions endured by dogs during and between races.

[75] Animal advocates have made pleas to Liberty Media CEO Greg Maffei to end GCI’s Iditarod sponsorship.