There has been uninterrupted interest in the thermodynamics of supercooled water ever since the pioneering experiments of Speedy and Angell revealed sharp increases in this substance response functions upon supercooling. One intriguing hypothesis postulates the existence of a metastable liquid-liquid transition at deeply supercooled conditions. Numerical studies have played an important role in the development of this idea. Old and novel studies supporting the existence of such a critical point will be discussed.