Graph grammars have found application in various domains, including computer science, biology, and social sciences, to model complex systems with graph-like structures. This paper presents a comprehensive survey of graph grammars, a formalism for defining graph-based models and transformations. The survey covers different approaches to graph rewriting such as gluing and connecting and also gives a briefing on different types of graph grammars, such as Node Replacement Graph Grammars, Context-Free Graph Grammars, Hyperedge Replacement Graph Grammars, Node Label Controlled Graph Grammars, Edge and Node controlled Embedding, and finally some new variants such as Graph Grammars with Regular Control, Jumping graph grammars, and graph grammars for basic biological modeling and computing. Finally, we discuss few open challenges in graph grammar research, such as efficient parsing and transformation algorithms, and suggest future directions for research in this field. This literature survey provides a valuable resource for researchers and practitioners interested in graph-based modeling and analysis.