What happens when a pinch of table salt is added to a cup of water? The dissociated cations (sodium ions) and anions (chloride ions) in the polar solvent distribute themselves in a correlated manner due to their electrical charges. Like charges repel each other and the opposite charges attract, and the pairwise electrostatic interactions can be long-ranged. As a result, the long-ranged correlations among the dissociated electrolyte ions lead to thermodynamic properties distinctly different from those for solutions containing uncharged solute molecules, although the electrolyte solution is overall neutral. When a foreign body such as a colloidal particle or a cylindrical pore is present in an electrolyte solution, the interfaces tend to be charged with one sign, and the oppositely charged ions (counterions) hover over near the interfaces. The amount of counterions near the interfaces is dictated by the balance between the strength of the attractive interaction between opposite charges and the loss of translational degrees of freedom of free counterions. Polyelectrolytes are no exception to this phenomenon. However, the conformational degrees of freedom of the charged macromolecules play an additional role in the way the various ions are correlated. Since an adequate description of ions surrounding a fluctuating macromolecule is quite complex, approximations are necessary. On the other hand, some rigorous results are known for the behavior of electrolyte solutions near rigid geometries such as planar interfaces, spheres, cylinders, pores, and lines. Therefore, it is useful to first gain an understanding of the behavior of electrolyte solutions around rigid geometric objects, before we address suitable models and approximations for charged macromolecules. The primary focus of this chapter is to collect the key concepts of electrostatic interactions in electrolyte solutions containing rigid geometric objects.