Many of them want to keep the business in the family, a challenge in itself. A main challenge is picking a successor, training that person to lead, and developing vision for the company. Most of the skills that are developed in a good leader aren't learned at some university. They are learned in the trenches. They are learned by observing others do the right things, and even by making mistakes.
Leaders have a responsibility to create a culture.
Some of this can be accomplished by telling stories, passing along the history and values. What is important is distilled through the lore and tradition that surrounds a family or a business. Everyone needs to share in how the dragon was slain or how the first big account was acquired. In some companies much of this history is not easily discovered. It is a responsibility of the leaders to tell the stories of the battles, the victories and the losses.