The new Focal Plane Array frontend for the WSRT, APERTIF, is expected to increase the survey speed of the WSRT by a factor of 20. This allows for efficient blind HI surveys of large areas of the sky out to a redshift of z=0.25, and pointed observations out to z=0.5, with an angular resolution of (1+z)*15 arcsec. These data will allow to investigate, for example, the cosmic evolution of $\Omega_{\rm HI}$ and the gas content of galaxies, the low-mass end and environmental dependence of the HI Mass Function, the evolution of the HI-based Tully-Fisher relation and constraints on the inter-galactic population of HI clouds. The expected number of detections at higher redshifts will be illustrated by actual data from the recently completed WSRT ultra-deep HI survey of two fields at z=0.2.