Cannot find module '@babel/core'

Try running this.

npm install @babel/core --save

babel changed their package so your babel-core will not be the same as @babel/core.

for those of you who use @babel/core alongside babel-node: i just installed @babel/core using npm i @babel/core --save-dev but when i tried to use babel-node it does not recognized the @babel/core package, i uninstalled @babel/core and installed it again using npm i @babel/core --save and it worked again!

The recent Babel upgrade to version 7 changed the namings of the node packages.

For instance, now you have to install

npm install --save-dev @babel/core @babel/preset-env

and

npm install --save-dev @babel/preset-react

to get it working with React. Then you can use these in your .babelrc file:

{
  "presets": [
    "@babel/preset-env",
    "@babel/preset-react"
  ]
}

Or as alternative, when not having a .babelrc, in your package.json:

...
"keywords": [],
"author": "",
"license": "ISC",
"babel": {
  "presets": [
    "@babel/preset-env",
    "@babel/preset-react"
  ]
},
"devDependencies": {
...

If you want to get more into it, you can checkout this recent Webpack + Babel + React setup.

I removed the existing npm uninstall babel-core babel-preset-env babel-preset-react

and added their new names npm install --save-dev @babel/core @babel/preset-env @babel/preset-react that's works for me as perfectly fine.