Compilers are not always correct due to the complexity of language semantics and transformation algorithms, the trade-offs between compilation speed and verifiability,etc.The bugs of compilers can undermine the source-level verification efforts (such as type systems, static analysis, and formal proofs) and produce target programs with different meaning from source programs. Researchers have used mechanized proof tools to implement verified compilers that are guaranteed to preserve program semantics and proved to be more robust than ad-hoc non-verified compilers. The goal of the dissertation is to make a step towards verifying an industrial strength modern compiler--LLVM, which has a typed, SSA-based, and general-purpose intermediate representation, therefore allowing more advanced program transformations than existing approaches. The dissertation formally defines the sequential semantics of the LLVM intermediate representation with its type system, SSA properties, memory model, and operational semantics. To design and reason about program transformations in the LLVM IR, we provide tools for interacting with the LLVM infrastructure and metatheory for SSA properties, memory safety, dynamic semantics, and control-flow-graphs. Based on the tools and metatheory, the dissertation implements verified and extractable applications for LLVM that include an interpreter for the LLVM IR, a transformation for enforcing memory safety, translation validators for local optimizations, and verified SSA construction transformation. This dissertation shows that formal models of SSA-based compiler intermediate representations can be used to verify low-level program transformations, thereby enabling the construction of high-assurance compiler passes.