  Spherically symmetric solutions of theories of gravity built one fundamental
class of solutions to describe compact objects like black holes and stars.
Moreover, they serve as starting point for the search of more realistic axially
symmetric solutions which are capable to describe rotating compact objects.
Theories of gravity that do not possess spherically symmetric solutions which
meet all observational constraints are easily falsified. In this article, we
discuss classes of exact and perturbative spherically symmetric solutions in
$f(T,B)$-gravity. The perturbative solutions add to the ones which have already
been found in the literature, while the exact solutions are presented here for
the first time. Moreover, we present general methods and strategies, like
generalized Bianchi identities, to find spherically solutions in modified
teleparallel theories of gravity.
