Topic modeling is one of the most powerful techniques in text mining for data mining, latent data discovery, and finding relationships among data, text documents. Researchers have published many articles in the field of topic modeling and applied in various fields such as software engineering, political science, medical and linguistic science, etc. There are various methods for topic modeling, which Latent Dirichlet allocation (LDA) is one of the most popular methods in this field. Researchers have proposed various models based on the LDA in topic modeling. According to previous work, this paper can be very useful and valuable for introducing LDA approaches in topic modeling. In this paper, we investigated scholarly articles highly (between 2003 to 2016) related to Topic Modeling based on LDA to discover the research development, current trends and intellectual structure of topic modeling. Also, we summarize challenges and introduce famous tools and datasets in topic modeling based on LDA. Latent Dirichlet Allocation (LDA) and Topic modeling: models, applications, a survey