The present state of the theory of strongly charged polyelectrolytes of the DNA type is reviewed. An infinitely long, uniformly charged cylinder immersed in a dielectric continuum is adopted as a model of DNA. Small mobile ions are treated as impermeable spheres. A comparison of the results of rigorous and approximate theoretical approaches to the description of this model shows that the self-consistent-field method, i.e., the Poisson-Boltzmann equation, is a reliable basis for deriving quantitative results. The theory of polyelectrolytes based on a solution of the nonlinear Poisson-Boltzmann equation is used to analyze the role played by electrostatic interactions in conformational changes in DNA. Transitions of two types are considered: a helix-coil transition and a transition between the ordinary right-hand-helix DNA (the B form) and the recently discovered left-hand-helix (the Z form). In the latter case the theory predicts a nonmonotonic behavior of the difference between the free energies of these conformations as a function of the salt concentration. It also predicts the existence of a critical point of a B-Z equilibrium for ionic strengths in the physiological region.