Portraiture has been a long, on-going tradition, firstly introduced in classics sculpture, to canvas painting and then to photography. If one will look closer, very little has changed with portraiture, and we refuse to accept the "selfie" as a work of art.
Some few, remarkable moments that come to mind in this history of portraiture is the introduction of the environmental portraiture, thanks to Arnold Newman; there's also the iconic instant photo headshots by Andy Warhol. And now we're in the 21st century, recycling the same aesthetics. No need to worry though, you don't have to fit in a certain style to keep being creative in portraiture. Just watch this video of awesome portrait photography ideas.
Preview image was taken from the video.