In birational geometry, log pairs are introduced for studying open varieties and for reducing problems to lower dimensional case. In this talk, I will explain that this framework can be used to study rational curves on varieties. I will introduce A^1-connectedness for log smooth pairs, i.e., the interior admits lots of rational curves which meet the boundary once. A typical example is a projective space with a smooth Fano hypersurface. Then I will discuss several joint works with Qile Chen as applications of A^1-connected varieties. One application gives a simple proof of general Fano complete intersections are separably rationally connected.