Holographic conformal blocks from interacting Wilson lines

We present a simple prescription for computing conformal blocks and correlation functions holographically in AdS$_3$ in terms of Wilson lines merging at a bulk vertex. This is shown to reproduce global conformal blocks and heavy-light Virasoro blocks. In the case of higher spin theories the space of vertices is in one-to-one correspondence with the space of ${\cal W}_N$ conformal blocks, and we show how the latter are obtained by explicit computations.