The obvious advantage is that you do not incur the oversized cost of inventory and warehousing, as well as being able to carry a theoretically infinite selection.
Drop shipping is a very successful and well known supplier chain technique, but not without its challenges. Most major retailers engage is some form of drop shipping or another. Especially in e-commerce, drop shipping and third-party marketplaces (effectively large-scale, transparent drop ship operations) are the primary drivers of oversized selection.
First, the cost of drop shipping is generally transferred to IT, instead of physical inventory and warehouse space. Product management is the first challenge. The number of products and suppliers typically increases significantly, therefore the complexity of managing products increases. Order management is also vital to ensuring orders are filled properly and customers are kept happy.