This paper provides a comprehensive survey of Latent Dirichlet Allocation (LDA) and topic modeling, covering their applications across various fields such as software engineering, political science, medical science, and geographical analysis. LDA is a probabilistic model used to discover hidden topics in a collection of documents. The paper reviews the development of LDA-based topic modeling from 2003 to 2016, highlighting key research trends, challenges, and notable tools and datasets. It discusses various applications of LDA, including source code analysis, opinion mining, event detection, image classification, and recommendation systems. The paper also explores different extensions of LDA, such as Dynamic Topic Models, Relational Topic Models, and Semi-Supervised Hierarchical LDA. It summarizes the challenges in topic modeling, such as image processing, topic visualization, group discovery, and user behavior modeling. The paper also introduces some of the most famous data and tools in topic modeling. The paper concludes that LDA is a powerful tool for latent topic discovery and has wide applications in various fields.This paper provides a comprehensive survey of Latent Dirichlet Allocation (LDA) and topic modeling, covering their applications across various fields such as software engineering, political science, medical science, and geographical analysis. LDA is a probabilistic model used to discover hidden topics in a collection of documents. The paper reviews the development of LDA-based topic modeling from 2003 to 2016, highlighting key research trends, challenges, and notable tools and datasets. It discusses various applications of LDA, including source code analysis, opinion mining, event detection, image classification, and recommendation systems. The paper also explores different extensions of LDA, such as Dynamic Topic Models, Relational Topic Models, and Semi-Supervised Hierarchical LDA. It summarizes the challenges in topic modeling, such as image processing, topic visualization, group discovery, and user behavior modeling. The paper also introduces some of the most famous data and tools in topic modeling. The paper concludes that LDA is a powerful tool for latent topic discovery and has wide applications in various fields.