W. J. Muller (Mueller), was born in Bristol, the son of a Prussian refugee who became curator of the Bristol Museum. He trained for two years under J. B. Pyne, a landscape painter based in Bristol. He exhibited at the RA from 1833 and became an important Bristol artist, reputed as a watercolourist. He also painted in Norfolk and Suffolk, and in 1834-5 travelled in Europe, especially Venice. In 1838-9 he travelled further around the Mediterranean, and in the latter year transferred his English base to London. In 1843-4 he travelled to Lycia, in modern Turkey with an archaeological expedition, and he also went to Egypt. He returned to Bristol in 1845 for health reasons, and died there from a heart condition, in September 1845. Rather belatedly, in 1893 a bust of Muller (by Nathan Branwhit) was placed in Bristol Cathedral as a memorial.
Towards the end of the 19th Century, Muller was considered one of the greatest painters of the English landscape, but today his best known pictures are of the Middle East and Venice.
Examples of Muller's work may be seen in Bristol. A rustic picture called Young Anglers is in the Lady Lever Art Gallery, and an identically titled picture is in the Walker Art Gallery, Liverpool. The Temple of Theseus (1830) is at the Towner Art Gallery, Eastbourne.