Truncated Toeplitz operators are compressions of usual Toeplitz operators to star-invariant (model) subspaces of $H^2$ in the disc: if $K_\Theta = H^2\ominus \Theta H^2$, then, for a function $\phi$ on the circle, the truncated Toeplitz operator $A_\phi$ is defined by the formula $A_\phi f = P_\Theta (\phi f)$ for functions $f$ in $K_\Theta$ such that $\phi f$ is square integrable. Here $P_\Theta$ is the projector onto $K_\Theta$. A systematic study of truncated Toeplitz operators was started recently by D. Sarason. In contrast to the classical Toeplitz operators, a truncated Toeplitz operator may be sometimes extended to a bounded operator on $K_\Theta$ even for an unbounded symbol $\phi$. The question, posed by Sarason, is whether boundedness of the operator implies the existence of a bounded symbol. We show that in general the answer to Sarason's question is negative, though it is positive for some classes of inner functions. The talk is based on a joint work with Isabelle Chalendar, Emmanuel Fricain, Javad Mashreghi and Dan Timotin.