Robert West was born in Waterford. His father was an alderman of that city. West Studied art in Paris under Boucher and Vanloo. He won first prize for drawing in the French Academy. West may have been in England before he went to Paris. There is mention of a picture alleged to have been drawn by him. The picture is entitled Thomas Smith and his family. It is signed and dated R. West fecit 1735. What is certain is that West did return to Ireland on completion of his studies in France and settled in Dublin. He was one of the most important figures in the development of Irish art.

Thomas James Mulvany, stated in a memoir of West's son that Robert West's chalk drawings from the living model 'have never been surpassed and perhaps but rarely equalled…They are infallible models for study and have produced more good draughtsmen, and have impressed finer notions of the human form, than have the works of any other artist in the last century.' West established a drawing school in George's Lane in the late 1730's. In 1757 the Dublin Society (later known as the Royal Dublin Society) established its own drawing school in Shaw's Court in Dame Street. It approached West to take on the position of Master at this school. He accepted the invitation and successfully taught at its premises for some years. However in 1763 he became mentally deranged. Jacob Ennis, one of West's former pupils, succeeded him in the post of Master and taught there until his death in 1770. West was again restored to the post. However he died in 1770. His son, Francis Robert West, succeeded him as Master and was succeeded in turn by his grandson, Robert Lucius West.