Minimal surfaces are zero mean curvature surfaces that appear as idealized soap films in nature. Given two curves one can ask for a minimal surface interpolating them. In this talk, we will first go through a proof involving tools of functional analysis, such as an inverse function to theorem for Banach spaces to show this can always be achieved if the curves are sufficiently close. Then we will go through a different idea using Fourier series expansions of the curves, to understand the shape of such a joining surface. we will also talk about this problem in the context of timelike minimal surfaces, and discuss some ways to find the maximum allowed distance between the curves up to which, a minimal surface exists. Most of this talk will be based on my master’s thesis supervisor, Rukmini Dey’s works, and in the end, we will also some of our joint work, in the context of time like minimal surfaces.