Mathematical description of biological processes such as gene regulatory networks or signalling pathways by dynamic models utilising ordinary differential equations faces challenges if the model parameters like rate constants are estimated from incomplete and noisy experimental data. Typically, biological networks are only partially observed. Only a fraction of the modelled molecular species is measurable directly. This can result in structurally non-identifiable model parameters. Furthermore, practical non-identifiability can arise from limited amount and quality of experimental data. In the challenge of growing model complexity on one side, and experimental limitations on the other side, both types of non-identifiability arise frequently in systems biological applications often prohibiting reliable prediction of system dynamics. On theoretical grounds this article summarises how and why both types of non-identifiability arise. It exemplifies pitfalls where models do not yield reliable predictions of system dynamics because of non-identifiabilities. Subsequently, several approaches for identifiability analysis proposed in the literature are discussed. The aim is to provide an overview of applicable methods for detecting parameter identifiability issues. Once non-identifiability is detected, it can be resolved either by experimental design, measuring additional data under suitable conditions; or by model reduction, tailoring the size of the model to the information content provided by the experimental data. Both strategies enhance model predictability and will be elucidated by an example application. [Includes supplementary material].