Thicket density is a novel measure of the complexity of a definable set. It bears striking resemblance to VC density, and it relates to the order property exactly the same way VC density relates to the independence property, yet we know of no concrete technical link between the two. It also admits a notion of degree in the same way Morley rank admits Morley degree. In this talk, we define thicket density, prove its basic properties, and state these tantalizing connections. Finally, we describe applications to both model theory and computability over abstract structures.