Due to the huge number of themes and plugins available, it’s impossible to answer clearly to this question.
Because it uses standard WordPress functions and does not add any extra tables, Polylang is compatible, out of the box, with a lot of themes and plugins.
However, complex themes and plugins sometime require some extra work to make them multilingual ready. Fortunately, more and more developpers are testing their themes or plugins in multilingual environments.
A few very complex plugins, sometime adding extra tables, may require a lot of extra work be compatible with Polylang.
We guarantee that Polylang works with the default Twenty themes. We also included extra code to support a few very popular plugins such as Yoast SEO, some Jetpack modules, YARPP…