when we use the blowup technique and bubbling analysis? what are the essence and pespective? could you give some examples to explain them or some reference？ thank you

In geometric analysis, I guess the first wellknown blowup argument was given in R. Schoen's solution to Yamabe problem. He used a Green function to blow up the metric near a point $x$ so that the punctured ball $B(x,r)\setminus \{x\}$ becomes an asymptotically flat end of a complete noncompact manifold. (The idea of Schoen comes from his study of "mass".) In this case, because the blowup factor is a positive function, the new metric differs from the original one only by a conformal change. In other cases, we usually use constants to blowup the metric because we would like to understand the metric itself, rather than its conformal class. For example, when studying geometric flows such as the Ricci flow or the mean curvature flow, "blowup" means to dilate the metric near singularities. The motivation is to "look into the detail" and "kill the lower order terms". In Perelman's work, he can prove that after a suitable dilation, every finitetime singularity of 3dimensional Ricci flow on a compact manifold must be a cylinder, ball or capped cylinder.(It's called Canonical Neighborhood Theorem.) On the other hand, there is also a blowdown argument which could be used to study the asymptotic behavior. This is an (partial) answer from geometric viewpoint. 

