Topaz itself is a natural mineral, but the blue color in almost all blue topaz sold today is not natural. The Gemological Institute of America (GIA) explains that colorless topaz is plentiful and that irradiation followed by heat treatment turns it into various shades of blue. In nature, topaz is most commonly colorless, and naturally strong blue stones are extremely rare.
According to GIA, these treatments have created a large market for inexpensive blue topaz since the 1970s, and today it is basically a mass-market gem. The starting material and the type of treatment determine which blue results, and the stable, uniform color makes treated stones easy to cut into standard sizes for jewelry. Blue topaz is also a December birthstone.
Source: GIA: Topaz Quality Factors
Image: Blue topaz, by Mauro Cateb, CC BY 2.0, via Wikimedia Commons.