PostCSS is compilation step for your CSS that supports a variety of plugins for everything from CSS4 syntax support to minification and fallback generation.
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PostCSS allows you to opt-in to the features you need with plugins. This allows you to set it up to behave exactly like Sass, with nesting, mixing, extends, and more. On the other hand, it allows you to use plugins by themselves for things like auto-prefixing, minification, and more. You can even set up your own custom "stack" of plugins to do exactly what you like.
Pro Doesn't force designers to learn a new syntax
Rather than learn a different syntax, PostCSS allows you to write in pure CSS.
PostCSS is 3-30 times faster than Sass (including libsass), Less, and Stylus
Con Harder to install and keep working
The immense flexibility of PostCSS plus its current rapid evolution makes it harder to install, configure and keep running than the more monolithic and mature preprocessors.
Con Some plugins need to run in a certain order
Some plugins can only work if initialized after some other plugins. For example, transforming and applying CSS variables needs to run before running a plugin which uses these variables inside conditional transformations.