ZnO single crystals, epilayers, and nanostructures often exhibit a variety of narrow emission lines in the spectral range between 3.33 and 3.35 eV which are commonly attributed to deeply bound excitons (Y lines). In this work, we present a comprehensive study of the properties of the deeply bound excitons with particular focus on the Y 0 transition at 3.333 eV. The electronic and optical properties of these centers are compared to those of the shallow impurity related exciton binding centers (I lines). In contrast to the shallow donors in ZnO, the deeply bound exciton complexes exhibit a large discrepancy between the thermal activation energy and localization energy of the excitons and cannot be described by an effective mass approach. The different properties between the shallow and deeply bound excitons are also reflected by an exceptionally small coupling of the deep centers to the lattice phonons and a small splitting between their two electron satellite transitions. Based on a multitude of different experimental results including magnetophotoluminescence, magnetoabsorption, excitation spectroscopy (PLE), time resolved photoluminescence (TRPL), and uniaxial pressure measurements, a qualitative defect model is developed which explains all Y lines as radiative recombinations of excitons bound to extended structural defect complexes. These defect complexes introduce additional donor states in ZnO. Furthermore, the spatially localized character of the defect centers is visualized in contrast to the homogeneous distribution of shallow impurity centers by monochromatic cathodoluminescence imaging. A possible relation between the defect bound excitons and the green luminescence band in ZnO is discussed. The optical properties of the defect transitions are compared to similar luminescence lines related to defect and dislocation bound excitons in other II-VI and III-V semiconductors.