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Recently, laser cooling methods have been extended from atoms to molecules. The complex rotational and vibrational energy level structure of molecules makes laser cooling difficult, but these difficulties have been overcome and molecules have now been cooled to a few microkelvin and trapped for several seconds. This opens many possibilities for applications in quantum science and technology, controlled chemistry, and tests of fundamental physics. This article explains how molecules can be decelerated, cooled and trapped using laser light, reviews the progress made in recent years, and outlines some future applications.