This paper provides a comprehensive survey of Latent Dirichlet Allocation (LDA) and topic modeling, focusing on their applications and developments from 2003 to 2016. LDA is a popular method in topic modeling, widely used in various fields such as natural language processing, text mining, and social media analysis. The authors investigate scholarly articles to understand the research trends, current trends, and intellectual structure of LDA-based topic modeling. They also summarize challenges and introduce famous tools and datasets in this field. The paper highlights the importance of topic modeling in computer science, particularly in text mining and natural language processing. It discusses the basic concepts of LDA, including its generative model, parameter estimation, and inference methods such as Gibbs sampling, expectation-maximization (EM), and variational Bayes inference. The authors review past work from 2003 to 2016, covering various extensions and applications of LDA, such as Author-Topic Model (ATM), Dynamic Topic Model (DTM), Labeled LDA (LLDA), MedLDA, and Relational Topic Models (RTM). They also discuss recent advancements in 2016, including bursty topic detection, personalized hashtag recommendation, and multi-modal social event tracking. The paper further explores the application of LDA in different scientific disciplines, including linguistic science, political science, medical and biomedical research, and geographical and location-based analysis. It provides a taxonomy of current approaches and significant research in these areas, highlighting the versatility and effectiveness of LDA in uncovering hidden structures and relationships in large datasets.This paper provides a comprehensive survey of Latent Dirichlet Allocation (LDA) and topic modeling, focusing on their applications and developments from 2003 to 2016. LDA is a popular method in topic modeling, widely used in various fields such as natural language processing, text mining, and social media analysis. The authors investigate scholarly articles to understand the research trends, current trends, and intellectual structure of LDA-based topic modeling. They also summarize challenges and introduce famous tools and datasets in this field. The paper highlights the importance of topic modeling in computer science, particularly in text mining and natural language processing. It discusses the basic concepts of LDA, including its generative model, parameter estimation, and inference methods such as Gibbs sampling, expectation-maximization (EM), and variational Bayes inference. The authors review past work from 2003 to 2016, covering various extensions and applications of LDA, such as Author-Topic Model (ATM), Dynamic Topic Model (DTM), Labeled LDA (LLDA), MedLDA, and Relational Topic Models (RTM). They also discuss recent advancements in 2016, including bursty topic detection, personalized hashtag recommendation, and multi-modal social event tracking. The paper further explores the application of LDA in different scientific disciplines, including linguistic science, political science, medical and biomedical research, and geographical and location-based analysis. It provides a taxonomy of current approaches and significant research in these areas, highlighting the versatility and effectiveness of LDA in uncovering hidden structures and relationships in large datasets.