Zero-knowledge Ethereum Virtual Machines (zkEVMs) must reconcile a fundamental contradiction: the Ethereum Virtual Machine was designed for transparent sequential execution, while zero-knowledge proofs require algebraic circuit representations. This survey provides the first systematic analysis of how existing major production zkEVM implementations resolve this tension through distinct constraint engineering strategies. We develop a comparative framework that maps the design space across three architectural dimensions. First, arithmetization schemes reveal stark trade-offs: R1CS requires compositional gadget libraries, PLONKish achieves elegance through custom gates that capture complex EVM opcodes in single constraints, while the homogeneous structure of AIR fundamentally mismatches the irregular instruction set of EVM. Second, dispatch mechanisms determine constraint activation patterns: selector-based systems waste trace width on inactive constraints, while ROM-based approaches trade memory lookups for execution flexibility. Third, the Type 1-4 spectrum quantifies an inescapable trade-off: the bit-level EVM compatibility of Type 1 demands significantly higher constraint complexity than the custom instruction sets of Type 4. Beyond cataloging implementations, we identify critical open problems across multiple domains: performance barriers preventing sub-second proving, absence of formal verification for constraint-to-EVM semantic equivalence, lack of standardized benchmarking frameworks, and architectural gaps in hybrid zkEVM/zkVM designs, decentralized prover coordination, privacy preservation, and interoperability.