Aside from being an excellent painter, what makes Rembrandt van Rijn so important?

Many say that Rembrandt van Rijn is one of the most important or greatest painters in all of history, just as they say Leonardo da Vinci was a great artist, but Leonardo did a variety of things (engineer, architecture, painting, sculpting, invent). What did Rembrandt do or who did he influence or what ideas did he p to earn him such a great role in history?