Topological phases of matter cannot be characterized by any 

pattern of symmetry-breaking, so describing phase transitions between 

them is a significant theoretical challenge. In the case of non-

Abelian phases, there are only a few examples of phase transitions 

that are theoretically understood. In this talk I will describe a 

series of phase transitions between well-known bilayer Abelian 

fractional quantum Hall (FQH) states -- the (ppq) states -- and a 

series of non-Abelian FQH states. An example of this transition is 

between the (330) state and the non-Abelian Z4 parafermion state, 

driven by increasing interlayer tunneling and/or interlayer repulsion. 

Previously used methods have failed because the transition from these 

states appears to be driven by the condensation of anyons. After 

presenting a recently developed effective field theory for the non-

Abelian states, I will explain how it can be used, along with other 

methods, to shed light on the nature of these transitions.