Heart rate monitors, how functional are wrist based monitors?

Your mileage will vary. Depends on how you wear the wrist sensor (how high/low on the wrist, how tight), your skin (color, hair, …), the sport (vibrations or not, loads on the arms/hands or not), ambient lighting (yes, even that - there can be interference with the sensor), and so on.

In general, for cycling, wrist-based optical sensors are not great. The combo of vibrations and load through the arms and hands create less-than-ideal conditions. Arm optical sensors (such as Scoche, Wahoo TICKR Fit or Polar OH1) and chest sensors are best for cycling.