Loop models are statistical mechanical models where the underlying degrees of freedom are loop configurations drawn on an underlying 2d lattice. When these models are tuned to their critical point and a continuum limit is taken, they can be described by a 2d CFT. These 2d CFTs are solvable, however unlike previously solved 2d CFTs they have a discrete, yet infinite, spectrum of primary fields. We will solve these models in the presence of a boundary. The spectrum can be determined analytically by studying annulus partition functions and this data can then be used in the crossing equations for correlators. With a known spectrum, the crossing equations are a set of linear equations for the coefficients in front of the conformal blocks. By combining analytic and numerical tools we can find analytic conjectures for these coefficients. This leads to analytic expressions for the correlators and hence we deem the model solved.