An active area of research in psycholinguistics concerns the cognitive mechanisms that are used to form syntactic dependencies in real-time sentence processing. Comprehenders make skilled use of working-memory resources to incrementally store and update syntactic structures (backward dependency formation) and use fine-grained probabilistic knowledge to anticipate the ways in which syntactic dependencies will eventually be resolved (forward dependency formation). While this broad picture is generally acknowledged, exactly how these processes play out in typologically diverse languages remains underexplored. In this chapter, we describe the various ways in which different grammatical systems pose diverse challenges for this general picture of sentence processing and present experimental research that addresses how core processes of backward and forward dependency play out in typologically diverse contexts. We argue that comparative sentence processing research presents evidence for shared cognitive mechanisms used for dependency formation across languages, but also points to several ways in which current theories need to be expanded to capture cross-linguistic variation.