This position paper gives an overview of the discussion that took place at FIPSE 2 at Aldemar Resort, east of Heraklion, Crete, in June 21-23, 2014. This is the second conference in the series "Future Innovation in Process Systems Engineering" (http://fi-in-pse.org), which takes place every other year in Greece, with the objective to discuss open research challenges in three topics in Process Systems Engineering. One of the topics of FIPSE 2 was the issue of "Linking Models and Experiments", which is described in this publication. Process models have been used extensively in academia and industry for several decades. Yet, this paper argues that there are still substantial challenges to be addressed along the lines of model structure selection, identifiability, experiment design, nonlinear parameter estimation, model validation, model improvement, online model adaptation, model portability, modeling of complex systems, numerical methods, software environments, and implementation aspects. Although there has been an exponential increase in the number of publications dealing with "modeling", the majority of these publications do not use sound statistical tools to evaluate the model quality and accuracy and also present modeling as a noniterative task. As a result, the models often have either too few or too many parameters, thus requiring trimming down or enhancing before they can be used appropriately. Also, this position paper argues that the models should be developed with a purpose in mind, as, for example, different models are needed for design, control, monitoring, and optimization.