Born in Bristol, the son of a Prussian refugee.  As a young man Muller was apprenticed to J.B. Pyne but the indentures were cancelled after two years.  He painted in and around Bristol, visited Wales and travelled up the Rhine to Switzerland, Venice, Florence and Rome.
He made many drawings and sketches on his travels, which he later worked up into finished paintings.
He was especially enthralled by Venice of which he painted many of his best pictures.
In 1839 he visited Greece, Egypt, Malta and Naples and later northern France and Turkey.
He is now best known for his Venetian and Middle Eastern scenes.