Algebraic Statistics is a relatively new field of research where tools from Algebraic Geometry, Combinatorics and Commutative Algebra are used to solve statistical problems. A key area of research in this field is the Gaussian graphical models, where the dependence structure between jointly normal random variables is determined by a graph. In this talk, I will explain the algebraic perspectives on Gaussian graphical models and present some of my key results on understanding the defining equations of these models. In the end, I will talk about the problem of structural identifiability and causal discovery and how algebraic techniques can be implemented to tackle them.