It has been well known that any closed, orientable 3-manifold can be obtained by Dehn surgery on a link in S^3. One of the most prominent problems in 3-manifold topology is to list all the possible lens spaces that can be obtained by a Dehn surgery along a knot in S^3, which has been solved by Greene. A natural generalization of this problem is to list all the possible lens spaces that can be obtained by a Dehn surgery from other lens spaces. Besides, considering surgeries between lens spaces is also motivated from DNA topology. In this talk, we will discuss distance one surgeries between lens spaces L(p,1) with p \geq 5 prime and lens spaces L(n,1) for integer n, correspondingly band surgeries from T(2,p) to T(2,n), by using Heegaard Floer d-invariant. This is a joint work with Zhongtao Wu.