Developmental Biology studies the processes whereby animals and plants grow and develop. One of the most studied scenarios in this discipline is the development of the neural tube upon Sonic Hedgehog signaling. We review several mathematical approaches that have been used to describe the former system in a quantitative way, paying attention to both their merits and their drawbacks. Experimental results suggest that transient dynamics can be quite important for the understanding of the patterning process. It has not been possible to fully replicate these dynamics by means of the available models yet, an important problem being to deal with the finite propagation speed of signaling interfaces. While continuous models relying on finite propagation speed mechanisms have been advocated elsewhere, we discuss here a spatially discrete multiscale model allowing to cope with this problem.