Given a Riemann surface $X$, a moduli space $M_X$ of vector bundles on $X$, and a theta line bundle $/Theta_X$ on $M_X$, sections of $/Theta_X$ are called "generalised theta functions". If $X$ varies in a family, the space of these functions spreads out to give a vector bundle on  the parameter space of the family. This vector bundle carries a flat projective connection. The algebro-geometric version was described by Hitchin.  I give an introduction to this connection, and discuss the question of its unitarity.