We survey the landscape of human operator mod- eling ranging from the early cognitive models developed in artificial intelligence to more recent formal task models developed for model-checking of human machine interactions. We review human performance modeling and human factors studies in the context of aviation, and models of how the pilot interacts with automation in the cockpit. The purpose of the survey is to assess the applicability of available state-of-the-art models of the human operators for the design, verification and validation of future safety-critical aviation systems that exhibit higher-level of autonomy, but still require human operators in the loop. These systems include the single-pilot aircraft and NextGen air traffic management. We discuss the gaps in existing models and propose future research to address them.