There are various jQuery plugins for filtering and sorting elements where the most popular ones are Isotope and Quicksand.

MixItUp is another great plugin to handle such tasks that deserves to be bookmarked.

While jQuery part decides which elements to show or hide, CSS3 transitions are used for animating them.

jQuery Filtering Plugin - MixItUp

The plugin plays nice with responsive + fluid layouts it is lightweight and works pretty fast.

There are many options for customization: effects, easing, their speed, etc. and it is very well-documented.

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