  We study half-BPS line defects in $\mathcal{N}=2$ superconformal theories
using the bootstrap approach. We concentrate on local excitations constrained
to the defect, which means the system is a $1d$ defect CFT with
$\mathfrak{osp}(4^*|2)$ symmetry. In order to study correlation functions we
construct a suitable superspace, and then use the Casimir approach to calculate
a collection of new superconformal blocks. Special emphasis is given to the
displacement operator, which controls deformations orthogonal to the defect and
is always present in a defect CFT. After setting up the crossing equations we
proceed with a numerical and analytical bootstrap analysis. We obtain numerical
bounds on the CFT data and compare them to known solutions. We also present an
analytic perturbative solution to the crossing equations, and argue that this
solution captures line defects in $\mathcal{N}=2$ gauge theories at strong
coupling.
