Nanoscale structures, including molecules, supramolecules, polymers, functionalized surfaces, and crystalline/amorphous solids, can commute between two or more forms, displaying contrasts in their nonlinear optical (NLO) properties. Because of this property, they have high potential for applications in data storage, signal processing, and sensing. As potential candidates for integration into responsive materials, scientists have been intensely studying organic and organometallic molecules with switchable first hyperpolarizability over the past two decades. As a result of this, researchers have been able to synthesize and characterize several families of molecular NLO switches that differ by the stimulus used to trigger the commutation. These stimuli can include light irradiation, pH variation, redox reaction, and ion recognition, among others. The design of multistate (including several switchable units) and multifunctional (triggered with different stimuli) systems has also motivated a large amount of work, aiming at the improvement of the storage capacity of optical memories or the diversification of the addressability of the devices.