The HALOGAS (Hydrogen Accretion in LOcal GAlaxieS) survey with the Westerbork Synthesis Radio Telescope is the most sensitive systematic survey of the diffuse neutral hydrogen component in nearby spiral galaxies so far. The 5-sigma column density sensitivity reached for the sample of 22 galaxies is ~10^19 atoms cm^-2 over the typical line width of the neutral gas in our target galaxies. The 3D observations are sensitive enough to perform detailed kinematical and dynamical analyses of the extended (vertical) disk structure of our targets. Additionally, we are able to provide a census of the complete cold neutral cloud population above the mass detection limit for individual objects of 10^5 solar masses on average. Our results are relevant in the context of theories describing star formation feedback on the gaseous interface of the galaxy disks with their surroundings, as well as gas accretion from the intergalactic medium. Most notably, we find that the presence of anomalous, slowly rotating extraplanar gas is related to the star formation surface density. I will present the consequences of our observations for the current accretion in local galaxies, and discuss the implied constraints on the accretion process more generally.