Considered as the most promising material to replace Al in ULSI thin film interconnects, Cu still demonstrates a rather poor electromigration (EM) behavior, with a surprisingly low EM activation energy, E-EM. A popular line of thought attributes this to fast surface/heterogeneous interphase boundary mass transfer. We present a totally different explanation. It is based upon recent progress in the theory of grain boundary (GB) grooving with an arbitrary GB flux [1], a specific model applying the general theory to EM [2] and new insight into the Cu EM literature data, in particular on the drift velocity (DV) EM tests. We show that (a) GB's are still most likely the major EM diffusion pathways in Cu, and (b) the major features of Cu EM can be rationalized in terms of the slit-like GB groove extension and merging. In this process, capillary force driven surface diffusion along a groove wall acts in effect as a ''healing'' mechanism, rather than as a parallel EM channel, or as a groove extension mechanism. Inserting the EM activation energy reported for Cu into this new model suggests that the surface diffusion is slow, with an activation energy above 2 eV most likely due to trace surface contaminations. The slow surface diffusion is seen as the major contributor to fast EM failures, implying that the full advantages of Cu can be realized if surface diffusion retardants are identified and eliminated. The issue is addressed in more detail and referenced extensively elsewhere [3]. The analysis in the present paper employs the most recent data for Cu and Cu(Sn) alloys.