Polymer (https://www.polymer-project.org) is a solution for the styles problem. You can pack each component with its own styles, complete with all its functionality. This allows for a very clean separation of concerns among components. Better than all other libraries that I have tried. I hope that web components take off, because it is a great way to build apps. Currently they are only supported in Chrome.
Moving data between components in Polymer, can be done with data binding. The bad thing is that it could get messy for complex applications. Is not terribly bad, but it could be better. What Polymer needs is a better way to move data between components. If that problem is solved, Polymer would be an excellent alternative to create any kind of apps.