  This text surveys cohomological properties of pairs $(U,f)$ consisting of a
smooth complex quasi-projective variety $U$ together with a regular function
on~it. On the one hand, one tries to mimic the case of a germ of holomorphic
function in its Milnor ball and, on the other hand, one takes advantage of the
algebraicity of~$U$ and $f$ to apply technique of algebraic geometry, in
particular Hodge theory. The monodromy properties are expressed by means of
tools provided by the theory of linear differential equations, by mimicking the
Stokes phenomenon. In the case of tame functions on smooth affine varieties,
which is an algebraic analogue of that of a holomorphic function with an
isolated critical point, the theory simplifies much and the formulation of the
results are nicer. Examples of such tame functions are exhibited.
