She has co-written tracks with Ed Sheeran, including "Thinking Out Loud" for which she won the 2016 Grammy Award for Song of the Year.

[7][better source needed] In 2021, she co-wrote the song "All of My Friends" from the Delta Goodrem album Bridge Over Troubled Dreams.

[citation needed][10] Having moved to Wales and graduated from the Royal Welsh College of Music and Drama, Wadge started performing at open mic sessions in Cardiff's Toucan Club and soon started developing a fanbase and gaining critical recognition.

She was quickly spotted and received encouragement from some of the big players in the city, among them Manics/Catatonia/Super Furry Animals producer Greg Haver, who recorded her debut mini-album, The Famous Hour.

[11] In 2002, Wadge won "Best Female Solo Act" at the annual Welsh Music Awards, ahead of Charlotte Church.

[citation needed] 2004 saw her release her first full album, WOJ (a play on her surname, which is often mispronounced), to critical acclaim.

In June 2004, she performed at London's Royal Albert Hall on a bill that included Jeff Beck and Jan Hammer, charted by Billboard magazine as one of the world's top-grossing concerts of the summer.