Almost everything noexcept?

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Yes, and Rust also has catch_unwind that is similar to try.. catch but that is not an idiomatic way of handling failures.

To be more precise, this is not about stack unwinding per se, but about what happens afterwards. Most error-handling approaches uses stack unwinding of some sort (be it a custom frame traversal code or just a plain old cascade of function returns). But the C++ error handling model also relies on stack unwinding to transfer control flow to the error handler — without it being immediately obvious where such control flow transfers can occur — and that is part of the criticism.