Fibonacci anyons exhibit the simplest kind of non-abelian statistics. I discuss various lattice models which have them as their quasiparticle excitations. These models include those based on string nets, and on self-avoiding loops. A mathematical byproduct of this work is that knot polynomials associated with the SO(3) Birman-Murakami-Wenzl algebra can be expressed in terms of the chromatic polynomial.