Police were called shortly before 8pm yesterday (March 10) to Listing Lane, near Gomersal.
A Fiat 500 and Toyota were travelling in opposite directions when the crash happened.
The driver of the Fiat 500, a 20-year-old woman, has been taken to hospital in a critical condition.
The driver of the Toyota was taken to hospital with non-life threatening injuries.
Police want to speak to anyone who saw what happened.
Officers are particularly keen to hear from anyone who has dash cam / CCTV footage of either car leading up to the collision.
Anyone with information is asked to contact police on 101 or use the contact us options at www.westyorkshire.police.uk/contactus quoting log 1541 of March 10.