Puw's works include pieces for unusual combinations of instruments, such as a tuba quartet or a trio consisting of harp, cello and double-bass, as well as more traditional forces such as solo baritone and piano, choir or orchestra.

Born in Parc (a village in Gwynedd near Bala),[3] Puw studied music composition at Bangor University with John Pickard, Andrew Lewis and Pwyll ap Siôn.

During this time, Puw wrote a concerto for oboe (premiered in 2006) and an orchestral piece, ... onyt agoraf y drws ..., which was first performed to critical acclaim at the 2007 Proms.

[3] In 1997, when the Eisteddfod was held in Bala, he won the Medal for a string quartet, Mecanwaith ("Mechanism") – this piece was later featured in S4C's television series Y Cyfansoddwyr ("The Composers").

[11] Puw has said that "The second movement is inspired by talkative people who won't let you contribute to a conversation", represented by a repeated row of 13 notes played until "it gets rather unbearable".

[11] His orchestral piece Reservoirs was inspired by a 1968 poem by R. S. Thomas about the drowning of Welsh valleys such as Tryweryn (a few miles from where Puw grew up) and Clywedog to provide water for England.

[18] In recent years, each movement of his lyrical Violin Concerto - Soft Stillness (2012–14) uses quotations from the 5th Act of Shakespeare's The Merchant of Venice as inspiration.

The repeated two-note motif introduced at the beginning and later the ascending scales are gradually concealed within thick blocks of orchestral textures.

In 2009 Hadau was commissioned by the National Eisteddfod of Wales to be performed alongside an installation by artist Christine Mills at the Lle Celf pavilion.

Scored for soprano, harp and narrator, the work was inspired by the strong Cerdd Dant tradition particularly found in rural communities of Meirionnydd and other parts of the country.

In 2017 Puw completed his first chamber opera Y Tŵr based on the play by the Welsh playwright, Gwenlyn Parry and to libretto by Gwyneth Glyn.

[20] Another piece requiring improvisation by performers was his commission for the 2001 Bangor New Music Festival, Trioled, which was written for ensemble (saxophone, guitar, harp, keyboard, cello, piano) and optional dancer.

[25] An ensemble piece, different light (for clarinet, violin, cello and piano) was "inspired by the idea of moving a picture from one place to another, be it to another house, or from one room to the next, or even from one wall to another.

The work features a series of chordal clusters, repeated descending modal scales and a playful tune, creating a humorous dialogue between the brass ensemble and the fairground organ.