The relation between language and thought – whether or not they function independently of each other – remains a mystery in philosophy and science. One approach for investigating this problem focuses on hierarchical processing as a fundamental feature of language and many other cognitive domains. Hierarchical processing involves the construction of temporally ordered sequences from integration of finite elements in embedded structures, such as the creation of sentences from letters, chord progressions from keys, formulas from symbols and operators, and complex actions from simple movements. Prominent theories propose that the hierarchical similarities between language and other cognition may derive from shared neural resources. These theories were tested in this dissertation with three different methodological approaches. In the first study, a behavioral dual task experiment revealed that simultaneous processing of language and music produced bidirectional interference of performance driven mostly by syntactic structural complexity rather than syntactic working memory demands. Cross-domain interference also occurred when syntactically critical words and keys temporally coincided. These novel findings support theoretical predictions of shared syntactic integration resources between language and music. In the second study, a Bayesian meta-analysis of neurostimulation experiments spanning six cognitive domains – action, artificial grammar, language, logic, math, and music – provided novel evidence of the potentially causal role of Broca’s area, based mostly on the pars opercularis subregion of the left inferior frontal gyrus (LIFG), as a shared neural resource for hierarchical processing. In the third study, a within-subjects neurostimulation experiment provided tentative evidence for potentially shared neural resources between language and math such that transcranial magnetic stimulation (TMS) of either the pars opercularis or the right intraparietal sulcus modulated performance of both linguistic and algebraic hierarchical processing. Taken together, these complementary studies support theories of shared resources across cognition and demonstrate the benefits of a multi-pronged research approach for exploring neurocognitive relations between language and thought.