Crowdsourcing is a major paradigm to accomplish works that require human skills, by paying a small sum of money and drawing workers all across the globe. However, crowdsourcing platforms are mainly ways to solve large amounts of relatively simple and independent replicated work units. A natural extension of crowdsourcing is to enhance the definition of work, and solve more intricate problems, via orchestrations of tasks, and via higher-order, i.e. allowing workers to suggest a process to obtain data rather than a returning a plain answer. This work proposes complex workflows, a data centric workflow model for crowdsourcing. The model allows orchestration of simple tasks and concurrency. It handles data and crowdworkers and provides high-level constructs to decompose complex tasks into orchestrations of simpler subtasks. We consider termination questions: We show that existential termination (existence of at least one terminating run) is undecidable excepted for specifications with bounded recursion. On the other hand, universal termination (whether all runs of a complex workflow terminate) is decidable (and at least in co−2EXPTIME) when constraints on inputs are specified in a decidable fragment of FO. We then address correctness problems. We use FO formulas to specify dependencies between input and output data of a complex workflow. If dependencies are specified with a decidable fragment of FO, then universal correctness (whether all terminating runs satisfy dependencies) is decidable , and existential correctness (whether some terminating runs satisfy dependencies) is decidable with some restrictions.