Ionic compounds conduct electricity in the molten state or when dissolved in a polar solvent, typically water. In these states, the strong electrostatic forces between ions are overcome, allowing the ions to become mobile. In the molten state, the fixed lattice structure breaks down, and ions can move freely, facilitating electric conduction. Similarly, in a solution, water molecules surround and separate the ions, creating an environment where ions can move and carry an electric current. The ability of ions to move in the molten or dissolved state enables the conductivity of electricity in ionic compounds under these conditions.