NuSTAR is the first focusing telescope with high sensitivity at hard X-ray energies (E>8 keV), and therefore close to the peak of the cosmic X-ray background (CXB). The serendipitous survey is the largest blind survey performed with NuSTAR, with ~13 sq. degrees of coverage (over the first 40 months), and has yielded a large sample of ~500 hard X-ray sources (mostly AGN, but also some Galactic objects). I will present X-ray and multi-wavelength properties of the NuSTAR survey sources, comparing to local hard X-ray samples (e.g., from Swift BAT), and highlighting the key synergies with other (e.g., XMM-Newton) serendipitous survey catalogs. In terms of the cosmic census of AGNs, an important aim is to identify and characterise the most highly obscured (Compton-thick) systems, which may contribute a large fraction of the overall growth of supermassive black holes, but are normally hidden from view by gas and dust. The NuSTAR survey is beginning to uncover new Compton-thick AGNs which were elusive at other wavelengths, thus informing AGN population models.