Abstract: For an oriented surface S, the Kauffman bracket skein algebra of S is an algebra generated by isotopy classes of framed links in the thickened surface S x (-1,1) modulo skein relations, and it quantizes the SL2 character variety of S. I will review various vector space bases of the skein algebra, and discuss the problem on the positivity of structure constants. I will spend enough time to give an elementary introduction, and towards the end I will briefly present recently known results, from quantum cluster algebras and mirror symmetry, from foams, and from quantized K-theoretic Coulomb branches. I hope to focus more on the last one, which is based on my joint work 2505.13332 with Dylan Allegretti and Peng Shan, which gives a monoidal categorification of the skein algebra of a genus zero punctured surface.