After 15 years with Capitol Records, Megadeth left the label in July 2000. According to Mustaine, the departure was due to ongoing tensions with Capitol management. Capitol returned the band's newest recordings and released a greatest hits album, Capitol Punishment: The Megadeth Years, with two new tracks: "Kill the King" and "Dread and the Fugitive Mind". In November, Megadeth signed with Sanctuary Records. The band returned to the studio in October to finish its next album, The World Needs a Hero, which was near completion when Megadeth joined the Maximum Rock tour six months earlier. Following the negative response to Risk, Mustaine fired Bud Prager and produced the album himself. The songs were written by Mustaine alone, except for "Promises", which had contributions from Pitrelli. Two days before the release of The World Needs a Hero, Megadeth appeared in an episode of VH1's Behind the Music showcasing Mustaine, Ellefson, several past members, and Mustaine's old Metallica bandmates James Hetfield and Lars Ulrich.
The World Needs a Hero was released in May 2001, and debuted at number sixteen on the Billboard 200. It was banned in Malaysia when the national government determined that the album's artwork was "unsuitable for the nation's youth". Consequently, the band canceled its August 2 concert in Kuala Lumpur. The album marked Megadeth's return to a more aggressive sound after the stylistic variations of its previous two albums, but critics felt it fell short of expectations. Mustaine compared the album to a huge ship at sea, turning and trying to right itself to get back on course. Its lead single, "Moto Psycho", reached number 22 on the Billboard Mainstream Rock chart.
A European tour with AC/DC in support of The World Needs a Hero began in mid-2001, followed by an American tour with Iced Earth and Endo in September. Mustaine allowed fans to choose the setlist in each American city. However, the tour was cut short following the September 11 attacks; all dates were canceled, including a DVD shoot in Argentina. The band instead played two shows in Arizona on November 16 and 17, which were filmed and released as Megadeth's first live release, Rude Awakening. That year, Killing Is My Business... and Business Is Good! was remixed and remastered; the reissue featured modified artwork and several bonus tracks.
Traditional heavy metal bands such as UFO, Black Sabbath, Budgie, new wave of British heavy metal (NWOBHM) bands such as Motrhead, Iron Maiden, and Diamond Head, and punk rock bands such as the Sex Pistols and Ramones had a significant influence on Megadeth's sound. Hard rock bands such as AC/DC and Led Zeppelin were also influential on the group's guitar style. Although the music has roots in punk, university professor Jason Bivins wrote that Megadeth followed the basic blueprint of Motrhead and Iron Maiden. He described the style as a mix of "the instrumental virtuosity of the NWOBHM with the speed and aggression of hardcore punk", while also drawing lyrical inspiration from the horror-obsessed punk band Misfits. Mustaine has also listed albums by the Beatles as recordings that influenced him.
Mustaine is the band's primary songwriter. He develops songs starting with a particular riff that, with modifications, becomes the central part of the song. He has said that song fragments are composed separately, and then the band makes a compact structure from them. Drummer Shawn Drover stated that Mustaine had saved many riffs over the years and that some recent material is based on those demo recordings. Ellefson stated that the band constantly creates new material, and that making a recording begins with exchanging ideas after which the band enters the studio and discusses the concept, direction, artwork, and song titles. The lyrics are usually written after the music is arranged. Discussing the band's lyrics, Mustaine said that many of the themes are derived from literature, such as the novels of George Orwell.
The music of Megadeth and its underground metal contemporaries from the 1980s featured harsh vocals, double bass drum patterns, staccato riffing, tremolo picking, and screeching lead guitar work; albums from this period were produced on low budgets. After forming Megadeth, Mustaine followed the thrash metal style of his previous band, Metallica, with more emphasis on speed and intensity. Megadeth's music is characterized by its neat instrumental performance, featuring fast rhythm sections, complex arrangements, and "snarling" vocals. When asked to describe Megadeth's guitar style, Mustaine answered: "When you go to a show and see a guitar player who just stands there, that's a guitar player. A thrash guitar player is a guy who plays like he wants to beat the guitar's guts out." Most of the songs are recorded in standard guitar tuning as Mustaine believes it to provide a superior melody to alternative methods of tuning.
During the band's early days, Mustaine was the rhythm guitarist, while Chris Poland played lead. Although Poland performed only on Megadeth's first two albums, music journalists Pete Prown and Harvey P. Newquist credit him with making the music more colorful because of his jazz influences. According to former Metal Maniacs editor Jeff Wagner, the band's songwriting techniques peaked with the fourth album, Rust in Peace, which he described as a "flurry of precision and fluidity, making good on Megadeth's claim to being the world's state-of-the-art speed metal band". Musicologist Glenn Pillsbury stated the guitar work on the album was a mixture of Mustaine's "controlled chaos" and the "technical brilliance" of Marty Friedman. Studio efforts released in the mid- and late 1990s featured songs with compact structures and less complicated riffing.
Megadeth's lyrics often focus on death, war, politics, and religion. The lyricism centers on nihilistic themes, but occasionally deals with topics such as alienation and social problems. The earliest releases featured themes such as occultism, graphic violence, and Satanism. Nuclear warfare and government conspiracy were preoccupations on albums such as Rust in Peace and Countdown to Extinction. During Megadeth's commercial peak, Mustaine elaborated on more personal themes such as addiction and intimate relationships. For the lyrics on Cryptic Writings, Mustaine said that he wanted to write songs that had more appeal to a wider audience. The title of United Abominations is a satiric play on the name of the United Nations; Mustaine criticized the organization's ineffectiveness on a number of songs on that album. Later albums contained lyrics in a similar vein.