Speech deepfakes are artificial voices generated by machine learning models. Previous literature has highlighted deepfakes as one of the biggest security threats arising from progress in artificial intelligence due to their potential for misuse. However, studies investigating human detection capabilities are limited. We presented genuine and deepfake audio to n = 529 individuals and asked them to identify the deepfakes. We ran our experiments in English and Mandarin to understand if language affects detection performance and decision-making rationale. We found that detection capability is unreliable. Listeners only correctly spotted the deepfakes 73% of the time, and there was no difference in detectability between the two languages. Increasing listener awareness by providing examples of speech deepfakes only improves results slightly. As speech synthesis algorithms improve and become more realistic, we can expect the detection task to become harder. The difficulty of detecting speech deepfakes confirms their potential for misuse and signals that defenses against this threat are needed.