I will firstly introduce the background and motivation of studying L-functions attached to exponential sums, which turns a geometric problem into a more arthmetic and analytic one. Then back in my case by applying Dwork's p-adic cohomoloy and p-adic differential equations I compute the Newton polygon for the L-functions under some combinatorial conditions. This explict Newton polygon gives a strong evidence that satisfies Daqing Wan's "Newton approaching Hodge" limit conjecture. If time permits, I will also introduce my recent work in the corresponding symmetric power L-functions and unit root L-functions, where an expected "Newton over Hodge" type statement will be obtained.