Beginning in the 19th century, however, the family’s wealth was nearly gone, and they were facing bankruptcy. The Grimaldis have been the rulers of Monaco since the 13th century. The Grimaldi family owns the majority of the land in Monte Carlo. The .85-square-mile principality sits between France and Italy. Monte Carlo is the capital of the small sovereign city-state of Monaco. Not sure how to prepare for your trip to the luxurious area? We have some tips for you. The whole attitude in Monte Carlo is different. The casinos are full of people wearing dresses and tuxedos, as well as people wearing shorts and flip-flops. Planning a trip to Monte Carlo to gamble in its casino? Then, you will need to dress differently than you would in Las Vegas. The very thought of the city along the French Riviera brings to mind luxury and high rollers.