ABSTRACT: I will discuss the generation of entanglement between an atom and a cavity field mode, and how one can measure that entanglement. Initially, I focus on the weak driving field limit, where the system just has a few photons in the cavity, and use the quantum trajectory formalism to calculate the atom-field entanglement using standard quantities like vonNeumann entropy. Then one considers what one can actually measure, and in this weak field limit, it turns out that a cross correlation between the transmitted and fluorescent light will yield the amount of entanglement. As it is difficult to access fully the fluorescent light, a three-level atom and polarization tricks are employed, using cavity enhancement of spontaneous emission, to access the entanglement via a cross correlation of two orthogonally polarized cavity modes. This makes the experiment easier to do, but now we have atoms and two modes, a tripartite system. I discuss the difficulties and possible remedies, as well as the connection to the general problem of characterizing entanglement in an open system. Finally, I'll discuss the strong driving field case. Throughout I'll make contact with the experiments of the group of Luis Orozco at U. Maryland/JQI with whom we work.