This thesis deals with the analysis of triangular relations which connect the dynamics of physical theories in infrared (IR) spectrum of energies. Corners of the IR triangle represent soft theorems, asymptotic symmetries and memory effects. In recent years, it was shown that connections between these ”echo” throughout many physical theories with massless particles. Here, research of two corners of the IR triangle is conducted for the case gravity; more precisely, it is shown that asymptotic symmetries and soft theorems are connected via Ward identity. Firstly, Carter-Penrose diagrams are constructed for Minkowski spacetime since these are fit for description of lightlike trajectories in asymptotically flat spaces. Future and past null infinity as three-dimensional surfaces at which massles particles end and begin their trajectories are rigorously defined and parametrised by appropriate coordinates. In fourth chapter, Bondi-Sachs metric is analysed and Einstein equations written in terms of metric coefficients. Boundary conditions which preserve asymptotic flatness are imposed and solutions to Einstein equations are found in spatial infinity. Using these solutions, structure of asymptotic generators of diffeomorphisms is analysed and it is observed that these imply the existence of infinite number of consereved charges associated with spacetime translations. The analysis of asymptotic symmetries is concluded with derivation of supertranslational Ward identity which connects the S-matrix elements with and without the insertion of soft graviton. In fifth chapter, formalisam of gravity as an effective field theory is introduced. Gravitational waves are briefly revised and certain variables defined in chapter four are physically interpreted. Here, third corner of the infrared triangle, that is, the gravitational memory effect, is also briefly touched upon. Chapter is concluded with quantisation of gravity as effective field theory. Finally, Weinberg’s soft graviton theorem is derived by using Feynman diagrams and it is shown that supertranslationalWard identity follows from this theorem.