In this perspective article, we focus on recent developments in the theory of charge effects in biological DNA-related systems. The electrostatic effects on different levels of DNA organization are considered, including the DNA-DNA interactions, DNA complexation with cationic lipid membranes, DNA condensates and DNA-dense cholesteric phases, protein-DNA recognition, DNA wrapping in nucleosomes, and inter-nucleosomal interactions. For these systems, we develop a theoretical framework to describe the physical-chemical mechanisms of structure formation and anticipate some biological consequences. General biophysical principles of DNA compaction in chromatin fibers and DNA spooling inside viral capsids are discussed in the end, with emphasis on electrostatic aspects.