Modern means contemporary or in the now. A beehive hairdo is not so modern, though depending on the wearer, it could still be hip.
When talking about time, modern is used to mean what's happening right now. Texting your friends rather than calling them is modern. A modern building is more likely to be made out of glass and steel than bricks. In art, however, modern has a more specific meaning, as it defines a style of art produced from the 1860s to the 1970s and includes everyone from Monet to Miro. To be correct, use contemporary to mean art that is being created now.