It is well established that the formation and condensation of Cooper pairs are the two key factors to induce superconductivity in condensed matter, however the ways for the Cooper pairs to form and condense are very different in distinct material systems. I will start from the very basic knowledge of the BCS theory, then extend to the cuprate and iron based superconductors, main from the experimental point of view. In the cuprate system, the superconductivity may arise by doping to the Mott insulator, and the normal states shows many abnormal properties. In the iron based superconductors, moderate correlation exists and multiband physics are involved. But both systems show the pairing in the strong coupling limit. I will show some interesting points which are at odd with the BCS theory, and illustrate that the correlation effect and repulsive interaction may be the common strings to form high temperature superconductivity at ambient pressure. A picture concerning the evolution from BCS to BEC type condensation is proposed.