In this talk we survey the known connections and evidence supporting the conjectured equivalence of the following three properties of a closed, connected, orientable, irreducible 3-manifold W: (i) W admits a co-oriented taut foliation; (ii) W has a left-orderable fundamental group; (iii) W is a Heegaard-Floer L-space. In particular, we discuss the relativisation of the conjectures which led to the confirmation of the conjecture for graph manifolds, and the subsequent open problems suggested by the work of Jonathan Hanselman, Jake Rasmussen, Sarah Rasmussen and Liam Watson.