### Automatic continued fractions are transcendental or quadratic

We establish new combinatorial transcendence criteria for continued fraction expansions. Let $\alpha =[0;{a}_{1},{a}_{2},...]$ be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients ${\left({a}_{\ell}\right)}_{\ell \ge 1}$ of $\alpha $ is not ‘too simple’ (in a suitable sense) and cannot be generated by a finite automaton.