There are several methods to synthesize zirconia nanoparticles, including sol-gel, hydrothermal, and precipitation techniques. The sol-gel method involves the transition of a solution system from a liquid 'sol' into a solid 'gel' phase. The hydrothermal technique uses high-pressure, high-temperature water to crystallize materials. Precipitation involves the chemical reaction of zirconium salts in a solution to form zirconia particles.