I've followed their business for a few years and the rate of growth has been incredible.
I think a big part of it is down to the quality of their products. Booking.com is fantastic to use, I book every hotel trip through their site and the experience keeps improving. Their SEO & PPC approach works well, they seem to rank #1 for every destination. Their conversion process from landing on site through to booking is great.
Would love to know more about them, wish they published details on their approach, growth engines, engineering etc.