Relative symplectic cohomology (Rel SH), which is defined by Umut Varolgunes, has various applications, including the proof of the big fiber theorems through ideal-valued measures, characterization of heaviness, and Mayer-Vietoris sequence. In this talk, I will recall the definition of Rel SH and explain the role of completion in its construction. I will then define relative Rabinowitz Floer homology as a mapping cone and present several computations. This talk is based on joint work in progress with Jun Zhang.