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The specific advantages of ion beams for application in tumor therapy are attributed to their different macroscopic and microscopic energy deposition pattern as compared to conventional photon radiation. On the macroscopic scale, the inverted dose profile with a Bragg peak and small lateral scattering allow a better conformation of the dose to the tumor. On the microscopic scale, the localized energy deposition around the trajectory of the particles leads to an enhanced biological effectiveness, typically expressed in terms of the relative biological effectiveness (RBE). Experimental investigations reveal complex dependencies of RBE on many physical and biological parameters, as e.g., ion species, dose, position in the field and cell or tissue type. In order to complement the experimental work, different approaches are used for the characterization of the specific physical and biological properties of ion beams. In a set of two papers, which are linked by activities within a European HORIZON 2020 project about nuclear science and application (ENSAR2), we describe recent developments in two fields playing a key role in characterizing the increased biological effectiveness. These comprise the biophysical modeling of RBE and the microdosimetric measurements in complex radiation fields. This first paper gives a brief introduction into these fields and then focuses on aspects of biophysical modeling of RBE, specifically on semi-empirical approaches that are currently used in treatment planning for ion beam therapy. It summarizes the status and recent developments of the Local Effect Model (LEM) and its conceptual framework and shows examples of model validation using recent experimental data. The model is compared to other approaches, e.g., to the Microdosimetric-Kinetic Model (MKM), that builds the bridge to the experimental microdosimetric work. © Copyright © 2020 Scholz, Friedrich, Magrin, Colautti, Ristić-Fira and Petrović.