This expository paper contains a detailed introduction to some important works concerning the Gauss-Bonnet-Chern theorem. The study of this theorem has a long history dating back to Gauss's Theorema Egregium (Latin: Remarkable Theorem) and culminated in Chern's groundbreaking work [$$14$$] in $$1944$$, which is a deep and wonderful application of Elie Cartan's formalism. The idea and tools in [$$14$$] have a great generalization and continue to produce important results till today.