A common problem in the context of linear parameter-varying (LPV) systems is how input-output (IO) models can be efficiently realized in terms of state-space (SS) representations. The problem originates from the fact that in the LPV literature discrete-time identification and modeling of LPV systems is often accomplished via IO model structures. However, to utilize these LPV-IO models for control synthesis, commonly it is required to transform them into an equivalent SS form. In general, such a transformation is complicated due to the phenomenon of dynamic dependence (dependence of the resulting representation on time-shifted versions of the scheduling signal). This conversion problem is revisited and practically applicable approaches are suggested which result in discrete-time SS representations that have only static dependence (dependence on the instantaneous value of the scheduling signal). To circumvent complexity, a criterion is also established to decide when an linear-time invariant (LTI)-type of realization approach can be used without introducing significant approximation error. To reduce the order of the resulting SS realization, an LPV Ho-Kalman-type of model reduction approach is introduced, which, besides its simplicity, is capable of reducing even non-stable plants. The proposed approaches are illustrated by application oriented examples.