  In this note we solve the twisted conjugacy problem for braid groups, i.e. we
propose an algorithm which, given two braids $u,v\in B_n$ and an automorphism
$\phi \in Aut (B_n)$, decides whether $v=(\phi (x))^{-1}ux$ for some $x\in
B_n$. As a corollary, we deduce that each group of the form $B_n \rtimes H$, a
semidirect product of the braid group $B_n$ by a torsion-free hyperbolic group
$H$, has solvable conjugacy problem.
