During the past years there has been renewed interest in the wide-bandgap II-VI semiconductor ZnO, triggered by promising prospects for spintronic applications. First, ferromagnetism was predicted for dilute magnetic doping. In comprehensive investigation of ZnO:Co thin films based on the combined measurement of macroscopic and microscopic properties, we find no evidence for carrier-mediated itinerant ferromagnetism. Phase-pure, crystallographically excellent ZnO:Co is uniformly paramagnetic. Superparamagnetism arises when phase separation or defect formation occurs, due to nanometer-sized metallic precipitates. Other compounds like ZnO:(Li,Ni) and ZnO:Cu do not exhibit indication of ferromagnetism. Second, its small spin-orbit coupling and correspondingly large spin coherence length makes ZnO suitable for transporting or manipulating spins in spintronic devices. From optical pump/optical probe experiments, we find a spin dephasing time of the order of 15 ns at low temperatures which we attribute to electrons bound to Al donors. In all-electrical magnetotransport measurements, we successfully create and detect a spin-polarized ensemble of electrons and transport this spin information across several nanometers. We derive a spin lifetime of 2.6 ns for these itinerant spins at low temperatures, corresponding well to results from an electrical pump/optical probe experiment.