DNA in the form of chromosomes is packaged by histones, proteins that help to compact the approximately 2m of DNA in our nuclei into a nuclear space of a few microns in extent. The combination of DNA, and the proteins and RNA which bind to it, is chromatin. I will describe recent theoretical work from my group on models for the architecture of chromatin in the mammalian cell nucleus. These models describe chromatin as "active matter", a term which emphasizes the central role of non-equilibrium (energy-consuming) processes, or "activity". Our results address several long-standing questions in nuclear architecture, among them the large-scale territorial organization of chromosomes and their non-trivial positioning patterns, suggesting a simple, yet general, framework within which they may be understood.