A class of nonlinear integrable PDEs admit some special weak solutions called ``peakons'', which are characterised by ODE systems, namely peakon lattices. The celebrated Toda lattice was originally obtained as a simple model for describing a chain of particles with nearest neighbor exponential interaction and has been generalized in different directions. Both of the peakon and Toda lattices could be regarded as isospectral deformations related to certain orthogonal functions. In fact, for some initial value problems, these lattices can be explicitly solved by use of inverse spectral method involving certain ``orthogonality", approximation problems and continued fractions. In this talk, I will illustrate this picture with some typical examples.