  A celebrated theorem of Pimsner states that a covariant representation $T$ of
a $C^*$-correspondence $E$ extends to a $C^*$-representation of the Toeplitz
algebra of $E$ if and only if $T$ is isometric. This paper is mainly concerned
with finding conditions for a covariant representation of a \emph{subproduct
system} to extend to a $C^*$-representation of the Toeplitz algebra. This
framework is much more general than the former. We are able to find sufficient
conditions, and show that in important special cases, they are also necessary.
Further results include the universality of the tensor algebra, dilations of
completely contractive covariant representations, Wold decompositions and von
Neumann inequalities.
