In this dissertation, I present a set of novel constraint-based thread-modular abstract-interpretation techniques for static analysis of concurrent programs. Specifically, I integrate a lightweight constraint solver into a thread-modular abstract interpreter to reason about inter-thread interference more accurately. Then, I show how to extend the new analyzer from programs running on sequentially consistent memory to programs running on weak memory. Finally, I show how to perform incremental abstract interpretation, with and without the previously mentioned constraint solver, by analyzing only regions of the program impacted by a program modification. I also demonstrate, through experiments, that these new constraint-based static analyzers are significantly more accurate than prior abstract interpretation-based static analyzers, with lower runtime overhead, and that the incremental technique can drastically reduce runtime overhead in the presence of small program modifications.