A common assumption in the shop scheduling literature is that the processing order of the operations of each job is sequential; however, in practice, there can be multiple connections and finish‐to‐start dependencies among the operations of each job. This paper studies flexible job shop scheduling problems with arbitrary precedence graphs. Rigorous mixed integer and constraint programming models are presented, as well as an evolutionary algorithm is proposed to solve large‐scale problems. The proposed heuristic solution framework is equipped with efficient evolution and local search mechanisms as well as new feasibility detection and makespan estimation methods. To that end, new theorems are derived that extend previous theoretical contributions of the literature. Computational experiments on existing benchmark datasets show that the proposed solution methods outperform the current state‐of‐the‐art. Overall, 59 new best solutions and 61 new lower bounds are produced for a total of 228 benchmark problem instances of the literature. To explore the impact of the arbitrary precedence graphs, lower bounds and heuristic solutions are generated for new large‐scale problems. These experiments illustrate that the machine assignment flexibility and density of the precedence graphs, affect not only the makespan, but also the difficulty of producing good upper bounds.