One of the most important properties of a mathematical model is the abilityto make predictions: to predict that which has not yet been measured. Suchpredictions can sometimes be obtained from a simple simulation, but that requiresthat the parameters in the model are known from before. In biology, theparameters are usually both not known from before and not identifiable, i.e.the parameter values cannot be determined uniquely from available data. Insuch cases of unidentifiability, the space of acceptable parameters is large, ofteninfinite in certain directions. For such large spaces, sampling-based approachesthat try to characterize the entire space have difficulties. Recently, a new type ofalternative approaches that circumvent this characterization problem has beenproposed: where one only searches those directions in the space of acceptable parametersthat are relevant for the uncertainty of a particular prediction. In thisreview chapter, these recently proposed methods are compared and contrasted,both regarding theoretical properties, and regarding user experience. The focusis on methods from the field of systems biology, but also methods from biostatistics,pharmacodynamics, and biochemometrics are discussed. The hope is thatthis review will increase the usefulness and understanding of already proposedmethods, and thereby help foster a tradition where predictions only are deemedinteresting if their uncertainties have been determined.