How to check if a string contains a substring in Bash

I have a string in Bash:

string="My string"

How can I test if it contains another string?

if [ $string ?? 'foo' ]; then
  echo "It's there!"
fi

Where ?? is my unknown operator. Do I use echo and grep?

if echo "$string" | grep 'foo'; then
  echo "It's there!"
fi

That looks a bit clumsy.

Answer

You can use Marcus's answer (* wildcards) outside a case statement, too, if you use double brackets:

string='My long string'
if [[ $string == *"My long"* ]]; then
  echo "It's there!"
fi

Note that spaces in the needle string need to be placed between double quotes, and the * wildcards should be outside.