© 2017 ACM. Digital microfluidics based on electrowetting-on-dielectric technology is poised to revolutionize many aspects of chemistry and biochemistry through miniaturization, automation, and software programmability. Digital microfluidic biochips (DMFBs) offer ample spatial parallelism, which is then exposed to the compiler. The first problem that a DMFB compiler must solve is resource-constrained scheduling, which is NP-complete. If the compiler is applied off-line, then long-running algorithms that produce solutions of high quality, such as iterative improvement or branch-and-bound search, can be applied; in an online context, where a biochemical reaction is to be executed as soon as it is specified by the programmer, heuristics that sacrifice solution quality to attain a fast runtime are used. This article describes in detail the algorithms and heuristics that have been proposed for resource-constrained scheduling, focusing on several recent contributions: path scheduling and force-directed list scheduling. It also discusses shortcomings and limitations of existing optimal scheduling problem formulations based on Integer Linear Programming and presents an updated formulation that addresses these issues. The algorithms are compared and evaluated on an extensive benchmark suite of biochemical assays used for applications, such as in vitro diagnostics, protein crystallization, and automated sample preparation.