  In this paper, we investigate the umbral representation of the Fubini
polynomials $F_{x}^{n}:=F_{n}(x)$ to derive some properties involving these
polynomials. For any prime number $p$ and any polynomial $f$ with integer
coefficients, we show $(f(F_{x}))^{p}\equiv f(F_{x})$ and we give other curious
congruences.
