Treatment with broadly neutralizing antibodies (bNAbs) has recently proven effective against HIV-1 infections in humanized mice, non-human primates, and humans. For optimal treatment, susceptibility of the patient's viral strains to a particular bNAb has to be ensured. Since no computational approaches are so far available, susceptibility can only be tested in expensive and time-consuming neutralization experiments. Here, we present well-performing computational models (AUC up to 0.84) that can predict HIV-1 resistance to bNAbs given the envelope sequence of the virus. Having learnt important binding sites of the bNAbs from the envelope sequence, the models are also biologically meaningful and useful for epitope recognition. Additional to the prediction result, we provide a motif logo that displays the contribution of the pivotal residues of the test sequence to the prediction. As our prediction models are based on non-linear kernels, we introduce a new visualization technique to improve the model interpretability. Moreover, we confirmed previous experimental findings that there is a trend towards antibody resistance for the subtype B population of the virus. While previous experiments considered rather small and selected cohorts, we were able to show a similar trend for the global HIV-1 population comprising all major subtypes by predicting the neutralization sensitivity for around 36,000 HIV-1 sequences -a scale-up which is very difficult to achieve in an experimental setting.