In this talk we will see how gauge theory helps to compute minimal genus function for second homology classes inside 4-manifolds. Based on adjunction inequality and Thom's generalised theorem, we will compute this function for CP^2#(-CP^2), CP^1xCP^1, T^4 and CP^2. Afterwards we will examine case the of CP^2 more closely (it was Thom's conjecture for a while, stating that (d-1)(d-2)/2 is minimal genus for class representing d times generator of second homology of CP^2).