The main problem is the conflict between Kate and Petruchio. Petruchio sets out to "tame" Kate who, prior to his arrival, flames every potential suitor to come near her. The question of how the problem is resolved is the interesting one, because much depends on our reading of Kate's character and motivation. She certainly shows all outward signs of obedience. From the moment that she agrees that the sun is the moon and the old man a young virgin, Kate shows her capitulation to Petruchio. Yet is she "tamed", or is she simply playing his game? Most people read Kate as highly intelligent, a match for Petruchio on all levels, so it is difficult to see Kate's apparent capitulation as being complete, with no tinge of irony or play. Even her speech at the end seems subtly ironic...she says she is "ashamed that women are so simple" as to offer war when they should offer peace. Even the final bit of this scene, where she says that women should place their hands under their husbands' foot, can be seen as both a sign of service and a step in a mental dance. There is no doubt that she has publicly acknowledged Petruchio's superiority, but why? Does she believe it? Does she think he does? I've seen this play staged differently, from a straight rendition to one with irony, where she seems in control to the end, making him come to her even as she sinks to place her hand beneath his foot. In claiming to have no power, she claims it.