  We develop the theory of presentable categories internal to an $\infty$-topos
$\mathcal{B}$. We provide several characterisations of these, including a
description in terms of the associated sheaves of $\infty$-categories as well
as an internal analogue of the Lurie-Simpson characterisation of presentable
$\infty$-categories. For the latter, we develop a theory of internal
filteredness and study the associated notion of accessible internal categories.
We furthermore establish various structural results about presentable internal
categories, such as adjoint functor theorems and a symmetric monoidal
structure. We use the latter to identify the $\infty$-category of presentable
$\infty$-categories which are tensored over $\mathcal{B}$ as a full subcategory
of the $\infty$-category of presentable internal categories in $\mathcal{B}$.
We provide two applications of our framework: in the first, we derive a general
version of Diaconescu's theorem for $\infty$-topoi. In the second, we
characterise dualisable objects in the $\infty$-category of modules over an
$\mathbb{E}_\infty$-ring in $\mathcal{B}$ as internally compact objects.
