As long as people have made art there have been portraits. Portrait painting is a genre in painting, where the intent is to depict a living animated creature, most often human. Traditional portrait paintings aimed at depicting the likeness physically of the subject. The impressionist period began to diverge from the traditionalist and focused on more than the likeness.
In the olden days, Traditional portrait paintings were done and painted of important people, like royals etc. In Europe, kings and queens had their own court painters, charged with painting the royal family and their various associated servants and attendants. Diego Velazquez is among the most well known of these court painters.
The Impressionists and Post-Impressionists began deconstructing ideas about the nature of portraiture. None were more revolutionary than Vincent Van Gogh and Paul Gauguin. The post-impressionists broke open traditional portraiture and the artists that followed them explored all possible avenues of representation and expression. Henri Matisse, Egon Schiele, Edvard Munch and most famously Pablo Picasso pushed the portrait in different directions at the beginning of the 20th century, focusing on different aspects- line, color, form, and most importantly psychology. For the first time for many artists, the inner psyche of the sitter was as important, if not moreso, as the likeness in a portrait.