Fermat's "Least Action Principle"
To understand the reason why this happens, you need to think in terms of Fermat's least action principle. The reason why light refracts is because it "optimises" its path. In other words, light takes the path of minimal time. This is the principle that was stated by Fermat, and if you do the mathematical analysis of it, which is not hard, you can derive Snell's law. In quantum mechanics this is explained by the infinitely many paths light takes, and the way in which the phasors add up to give the most probable path.
When light falls vertically on the interface of two media, the straight through path is the shortest path from time point of view. So there is no need for light to divert its direction. Of course, some of it will be reflected back out. For example if it is air-to-glass, I think about 4% will be reflected and the rest will be transmitted.
As for the question "why light slows down", it has been discussed elsewhere in this forum.