There are thousands of species and varieties of begonia. Plant books used to divide them into three major groups: tuberous, rhizomatous, and fibrous-rooted. Currently, however, they are more commonly divided into even more groups.
They are mostly evergreen, perennials grown as houseplants and out of doors in zones 9 and higher. Many are grown for their beautiful leaves while many others are known for their flowering.
Cane-stemmed begonias are mostly upright with straight, upright, bamboo looking stems.
The rhizomatous begonias are a varied class with leaves growing direct from creeping rhizomes. This group may or may not include the Rex begonias grown for their foliage. Some categorize the Rex as a separate group.
Shrub-like begonias have more closely branched growing and are grown for bedding plants. This group may (or may not) include winter-flowering begonias grown for their colorful flowers that peak in the winter.
Finally (maybe) there are the tuberous begonias which include tuberhybrida, multiflora and pendula groups. These die back to tubers in the winter and have large, showy flowers in summer.
Most begonias like bright light but none like full sun, good, loose soil and moderate watering during the flowering season. Good drainage is important. The roots of all are shallow. Cut back on watering during the winter (unless it is a winter-flowering).
Fertilize once a month with a balanced fertilizer. Winter-flowering like no-nitrogen, high phosphorous fertilizer. With such a diverse group of plants specific needs will vary.
Propagation also differs for the different groups. Some can be propagated by seeds, some by cuttings, and some by tuber cuttings. The Rex can be propagated by leaf cuttings (invert the leaf on soil and cut the veins - new plants will grow where the vein cuts touch the soil.)