[5][6] The ship's maiden voyage was originally scheduled for 3 February 2001, a 14-day cruise from Port Everglades in Fort Lauderdale through the Panama Canal before arriving in San Diego for her inaugural season.

[8][7] Her inaugural season also included cruises to Hawaii[10] before she headed to Alaska in summer 2001, joining fleet-mate Mercury.

[11] Since 2002, she has also cruised to South America,[12] Antarctica,[13] the Caribbean from San Juan, Puerto Rico[14] and Fort Lauderdale,[15] and Europe from Harwich[16] and throughout the Mediterranean.

Months following her delivery, Celebrity reported Infinity began experiencing problems with a faulty ball bearing in the ship's starboard propulsion unit; it necessitated an emergency dry dock repair in June 2001 in Victoria, British Columbia, which resulted in cancelled sailings.

[29][30] In April 2002, more dry dock repairs were made to the ship's propulsion pods, as they were reportedly showing premature wear, preventing her from cruising at maximum speed.

[31] In a third dry dock in February 2003, Celebrity had all ball-bearing units on Infinity replaced, forcing the cancellation of two sailings.

[36] Numerous unsuccessful repairs led Royal Caribbean to file a lawsuit against Rolls-Royce and Alstom in August 2003 for $300 million to recover lost revenue and the costs associated with the faulty pods on all four Millennium-class ships.