To keep them blooming well, fertilize every other week. While they aren't bothered by many insect problems, tuberous begonias can develop powdery mildew. This is most likely during periods of high humidity and cool weather. Powdery mildew will give the leaves a gray, dusty appearance. At the first signs of this problem, increase air circulation and spray with a broad-spectrum fungicide.
Tuberous begonias do go dormant even when they are growing indoors.
At that point, remove the browned tops and store the tuber for 3-4 months, or until spring. Begonia tubers should be stored where it is cool, but not freezing and dry. They can either be left in the soil or unearthed and stored in vermiculite. Check on them every few weeks and mist lightly if they are drying to the point of shriveling. Most gardeners know them as wonderful bedding plants.