npm install doesn't save dependency to package.json

npm install without arguments installs all dependencies (and dev dependencies) listed in the package.json file.

npm install --production installs all the dependencies (but no dev dependency)

npm install <package> installs a package and its dependencies.

npm install <package> --save installs a package and its dependencies, and adds it in the package.json file.

Edit: Since npm 5, --save is implied.