  In this work we launch a systematic theory of superconformal blocks for
four-point functions of arbitrary supermultiplets. Our results apply to a large
class of superconformal field theories including 4-dimensional models with any
number $\mathcal{N}$ of supersymmetries. The central new ingredient is a
universal construction of the relevant Casimir differential equations. In order
to find these equations, we model superconformal blocks as functions on the
supergroup and pick a distinguished set of coordinates. The latter are chosen
so that the superconformal Casimir operator can be written as a perturbation of
the Casimir operator for spinning bosonic blocks by a fermionic (nilpotent)
term. Solutions to the associated eigenvalue problem can be obtained through a
quantum mechanical perturbation theory that truncates at some finite order so
that all results are exact. We illustrate the general theory at the example of
$d=1$ dimensional theories with $\mathcal{N}=2$ supersymmetry for which we
recover known superblocks. The paper concludes with an outlook to 4-dimensional
blocks with $\mathcal{N}=1$ supersymmetry.
