  We give a survey of our previous work on relatively minimal isotrivial
fibrations $\alpha \colon X \to C$, where $X$ is a smooth, projective surface
and $C$ is a curve. In particular, we consider two inequalities involving the
numerical invariants $K_X^2$ and $\chi(\mathcal{O}_X)$ and we illustrate them
by means of several examples and counterexamples.
