Domain experts are increasingly employing machine learning to solve their domain-specific problems. This article presents to software engineering researchers the six key challenges that a domain expert faces in addressing their problem with a computational workflow, and the underlying executable implementation. These challenges arise out of our conceptual framework which presents the �route� of transformations that a domain expert may choose to take while developing their solution. To ground our conceptual framework in the state of the practice, this article discusses a selection of available textual and graphical workflow systems and their support for the transformations described in our framework. Example studies from the literature in various domains are also examined to highlight the tools used by the domain experts as well as a classification of the domain specificity and machine learning usage of their problem, workflow, and implementation. The state of the practice informs our discussion of the six key challenges, where we identify which challenges and transformations are not sufficiently addressed by available tools. We also suggest possible research directions for software engineering researchers to increase the automation of these tools and disseminate best-practice techniques between software engineering and various scientific domains.