  We prove CLTs for biased randomly trapped random walks in one dimension. In
particular, we will establish an annealed invariance principal by considering a
sequence of regeneration times under the assumption that the trapping times
have finite second moment. In a quenched environment, an environment dependent
centring is determined which is necessary to achieve a central limit theorem.
As our main motivation, we apply these results to biased walks on subcritical
Galton-Watson trees conditioned to survive and prove a tight bound on the bias
required to obtain such limiting behaviour.
