Varroa
Varroa mites need to be controlled really strictly as they will decimate a hive in around two years if left to there own devices.
They also carry a virus called deformed wing virus, as the name suggests it deforms the wing in the pupa stage, just before it is about to emerge from the cell, and so shorting its life by half, no wings = no flying = no food to forage = so the the whole colony suffers from starvation eventually.
What you can do in the winter months is apply some thing called Oxalic acid which you make up with a little sugar and some water, get 5 mils in a syringe and trickle it down each seam of bees.
You do this in deepest winter when there is very little brood and the bees cluster.
You can also sprinkle icing sugar onto the bees during each manipulation, it only takes a few minutes to do so theres no excuse!