Currently I use Eclipse to develop my AEM application. I do that because Eclipse has a plugin that pushes any code changes to the AEM Author instance running in the background.
Is there such a solution for Intellij?
IntelliVault will allow you to upload content (including Sightly, JSP, clientlib resources, etc.) to your AEM instance from your IDE. It's very similar to the VaultClipse plugin for Eclipse.
Both of them use FileVault (VLT) behind the scenes.