Current speech translation systems, while having achieved impressive accuracies, are rather static in their behavior and do not adapt to real-world situations in ways human interpreters do. In order to improve their practical usefulness and enable interpreting-like experiences, a precise understanding of the nature of human interpreting is crucial. To this end, we discuss human interpreting literature from the perspective of the machine translation field, while considering both operational and qualitative aspects. We identify implications for the development of speech translation systems and argue that there is great potential to adopt many human interpreting principles using recent modeling techniques. We hope that our findings provide inspiration for closing the perceived usability gap, and can motivate progress toward true machine interpreting.