How does limewater get turned into limestone?

Limewater is a solution of calcium hydroxide, and limestone is calcium carbonate. A common test for carbon dioxide gas is the "limewater" test, in which a gas is bubbled into limewater, an aqueous solution fo calcium hydroxide, Ca(OH)2, and the solution turns cloudy due to the formation of an insoluble precipitate. The CO2 reacts with water to make H+ and HCO3-, both of which neutralize the OH- and produce CO3^2- which reacts with Ca2+ to make insoluble CaCO3, also called "limestone".