At least in Catholic liturgy this gesture is still alive and well, and I'd presume similar rituals are present in other rites as well. Some people put their first at their breast during the “Lord, I am not worthy that you should enter under my roof, but only say the word and my soul shall be healed“ (a prayer recited just before the priest takes communion and completes the sacrifice of the Eucharist), myself included, but most common still is striking your breast thrice during the “Confiteor“, a prayer said during the early part of Mass (when it's not substituted by the Kyrie) that includes the words “through my fault, through my fault, through my most grievous fault“ at which it is customary to strike your breast at each fault. Also at Tridentine Masses (i.e. performed in the rites that were common before the liturgical reforms of the 60s) some people also strike their breast thrice during the Eucharist.

Striking your breast was (is?) seen as an expression of sorrow and grief, and by extension penance. In the Catholic context it's certainly very old, being mentioned as early as St Augustine of Hippo (d. 430), and the Bible itself knows the gesture as well (e.g. Luke 18:13).

I don't know when or why the gesture ceased to be performed outside of a ritualistic context, at least in the West, but during the High Middle Ages it was still done, though “[s]uch gestures occur rather more frequently in French texts than in English, and they are generally performed by women“ (J.A. Burrow: Gestures and Looks in Medieval Narratives, p. 40) whereas the biblical text shows it being done by men too. The other examples of such gestures Burrow mentions are things like tearing your clothes or scratching your cheeks in grief, things that would indicate mental illness today but appear to have been common at least until the Middle Ages. I'm on my phone so I can't research any further, but I hope that that is at least a good starting point.

e: starting point, not strong point