One of the hallmark features of fractional quantum Hall liquids is the existence of chirally propagating edge modes at their boundary, whose presence has been an invaluable tool for probing the system’s exotic properties, most notably the presence of fractionally charged quasiparticles with anyonic exchange statistics. During this talk, I’ll describe how corrections to Wen’s chiral Luttinger liquid, the golden-standard for the description of these edge modes, emerge in systems such as anharmonically confined quantum Hall fluids or small atomic fractional quantum Hall states on a lattice. In particular, mode dispersion and non-linearities give rise to intriguing new features, such as solitons propagating along the boundary, quantum blockaded dynamics leading to the possibility of generating non-classical states of the edge, and bistable behaviors.