The chapter introduces first the functional framework corresponding to the spectral collocation method based on Laguerre functions. The main advantage of these functions is the fact that they decrease smoothly to zero at infinity along with their derivatives. We speculate this behavior in imposing boundary conditions at large distances. On the half-line we solve high order eigenvalue problems, linear as well as some genuinely nonlinear third and fourth order boundary value problems. The applications come from fluid mechanics, i.e., Blasius, Falkner-Skan, density profile equation, Ekman boundary layer etc. and foundation engineering. Consequently, we avoid the empiric domain truncation coupled with various numerical technique (mainly shooting) as a strategy to solve such problems. Some second order eigenvalue problems along with singularly perturbed boundary value problems are also considered. A special attention is payed to the influence of the scaling parameter (which maps the half-line into itself) on the repartition of the Laguerre nodes. We manually tune this geometrical parameter in order resolve narrow regions with high variations of solutions, i.e., the so called boundary or interior layers. Consequently, no domain decomposition, domain truncation and shooting have been used in our numerical experiments. Based on the pseudospectra of two GEPs we comment on limitations of the linear hydrodynamic stability analysis. We also observe that the non-normality of a spectral method depends on the discretization (method itself) and at the same time on the bases of functions (polynomials) used.