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WebAssembly is designed to be an alternative to JavaScript that is a safe, portable, and efficient compilation target for a variety of languages. The performance of high-level languages depends not only on the underlying performance of WebAssembly, but also on the quality of the generated WebAssembly code. In this paper, we identify several features of high-level languages that current approaches can only compile to WebAssembly by generating complex and inefficient code. We argue that these problems could be addressed if WebAssembly natively supported first-class continuations. We then present Wasm/k, which extends WebAssembly with delimited continuations. Wasm/k introduces no new value types, and thus does not require significant changes to the WebAssembly type system (validation). Wasm/k is safe, even in the presence of foreign function calls (e.g., to and from JavaScript). Finally, Wasm/k is amenable to efficient implementation: we implement Wasm/k as a local change to Wasmtime, an existing WebAssembly JIT. We evaluate Wasm/k by implementing C/k, which adds delimited continuations to C/C++. C/k uses Emscripten and its implementation serves as a case study on how to use Wasm/k in a compiler that targets WebAssembly. We present several case studies using C/k, and show that on implementing green threads, it can outperform the state-of-the-art approach Asyncify with an 18% improvement in performance and a 30% improvement in code size.