It's technically not illegal for women to drive in Saudi Arabia, it's actually just a religious custom, based on an archaic interpretation of Islamic texts.
However, women caught driving can face charges of "disturbing public order". The punishment for such an offence can range from jail time through to public lashings.
What's even worse is that the women in question and their families often face death-threats, and end up losing their jobs and being driven out of their homes.
Drivers in Saudi Arabia are required to apply for a licence from their local authority, and these governmental departments take customs so seriously that they refuse to issue driving licenses to women point blank.
Here's a pretty cool TedTalk given by Saudi activist Manal al-Sharif about the civil rights struggle that women are facing regarding this issue: