We develop an ontological interpretation for the electromagnetic field. We shall see that the wave functional has a natural interpretation as the probability density for a given field configuration. The electromagnetic field is therefore to be regarded as a “field” (always) without a particle-like nature. In developing a model of the electromagnetic field as a continuous field distribution, it becomes necessary to explain how, in interactions with matter, the field manifests itself in a descrite particle-like way. To this end we describe in detail the photoelectric and Compton effects, usually considered as experimental evidence for the particle-like nature of the electromagnetic field. As illustrations of our model, we consider two experiments which over the years have played a central role in conceptual discussions of the quantum theory: the two-slit and EPR experiments.