Tablets, phones, laptops. The new 3 promises to be mobile friendly from the start.
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There is now just one percentage-based grid for Bootstrap 3. Customize for fixed widths.
Improved support for mixins make the new Bootstrap 3 easier to customize.
In simple terms, a responsive web design figures out what resolution of device it's being served on. Flexible grids then size correctly to fit the screen.
The new Bootstrap 3 promises to be a smaller build. The separate Bootstrap base and responsive.css files have now been merged into one. There is no more fixed grid, only fluid.