Antimicrobial peptides (AMPs) have been proposed as a novel class of antimicrobials that could aid the fight against antibiotic resistant bacteria. The mode of action of AMPs as acting on the bacterial cytoplasmic membrane has often been presented as an enigma and there are doubts whether the membrane is the sole target of AMPs. Progress has been made in clarifying the possible targets of these peptides, which is reported in this review with as focus gram-positive vegetative cells and spores. Numerical estimates are discussed to evaluate the possibility that targets, other than the membrane, could play a role in susceptibility to AMPs. Concerns about possible resistance that bacteria might develop to AMPs are addressed. Proteomics, transcriptomics, and other molecular techniques are reviewed in the context of explaining the response of bacteria to the presence of AMPs and to predict what resistance strategies might be. Emergent mechanisms are cell envelope stress responses as well as enzymes able to degrade and/or specifically bind (and thus inactivate) AMPs. Further studies are needed to address the broadness of the AMP resistance and stress responses observed.