Wright has filled in as host of "The Madeleine Brand Show" on Southern California Public Radio, On Point on NPR, and the weekend edition of All Things Considered.

[34] Wright has covered the Holy See and the Catholic Church for ABC News since the final years of Pope John Paul II.

He reported from Rome during Pope John Paul's final days and the conclave that followed,[35] part of the ABC News team that shared a 2006 Alfred I. duPont–Columbia University Award.

[37] Wright has traveled on multiple trips with Popes Benedict and Francis in Europe, the Middle East,[citation needed] Africa,[38][39][40] and the Americas.

[59][60][61] On February 26, 2020, ABC News suspended Wright, who was video taped without his knowledge in a bar by Project Veritas complaining about the network's coverage.

He also self-identified as a socialist and complained about the fluffy content on ABC, giving as an example Walt Disney characters on Good Morning America.

"[65][66] On a shareholder call, Disney CEO Bob Chapek elaborated: "He (Wright) said some things that made us question his objectivity and obviously when you're reporting the news, there's no place for someone who's got a heavily subjective opinion.

Erik Wemple of the Washington Post wrote: "If ABC News has any concerns about Wright’s alleged bias — even the appearance of such — then it should present the evidence.

"[69] Wright met his wife, former Sky News producer Victoria Brannigan, in Rome when they were both covering the funeral of Pope John Paul II.