Packing of nucleic acids inside (naturally occurring) confined spaces presents an intriguing problem of compacting a long and highly charged polymer into a small space possibly crowded with other particles (proteins). For example, viruses have a large amount of genomic information that is encoded in nucleic acids packed in small spaces resulting in high densities of matter. The arising interactions are coupled to the confinement giving a more complex phase diagram than expected in bulk. In this work we study the problem of packing nucleic acids in confined spaces in the context of physical virology. First, we study compacted states of DNA including condensed DNA in cells and confined DNA in bacteriophage capsids. We apply polymer and liquid crystal theory along with mean field approximations for the bending energy to characterize the state of DNA. The resulting framework is used to explain in vivo ejection of DNA from a bacteriophage into a Gram-positive bacteria based only on thermodynamic considerations, without invoking any active cellular mechanisms. The packing mechanism for DNA with condensing proteins in adenoviruses is studied by comparing Langevin dynamics simulations of effective particle models, representing condensing proteins, with experimental data. The DNA is found to act as an effective medium for condensing core protein interactions. A backbone of DNA linking the condensing proteins is not needed to explain the experimental results. To further explain such systems, we construct a full model of packed polymer and condensing proteins inside spherical confinement using Langevin dynamics. Internal organization of condensing particles shows that they tend to cover themselves with the DNA polymer which provides an effective medium for interactions with other condensers, confirming the applicability of our effective model for core particle organization in adenoviruses. Crowding of the viral interior and confinement influences the conformation of the DNA and protein, facilitating more direct contacts between the DNA polymer and the condensing particles, and modifying the interactions between them. Our model is able to explain the general internal organization of adenovirus cores, and provide insight into packing of genetic material in similar systems.