Debugging Rust is available via an additional extension in Visual Studio Code. Install it by running ext install vadimcn.vscode-lldbin the command window (Ctrl + P/cmd + P).
On Windows, debugging is limited thanks to its incomplete LLVM support. However, the extension will prompt you to automatically install several things. Additionally, install Python 3.6 and add it to %PATH%. With these dependencies installed, it worked well for us (in March 2019).