This work offers a thorough analysis of topic modeling using Nonnegative Matrix Factorization (NMF), a potent method that is frequently employed to identify significant themes and patterns in sizable unstructured datasets. NMF has become a vital tool in domains such as document clustering, social network analysis, bioinformatics, and natural language processing by breaking down data into interpretable components. Important NMF variations are covered in this review, such as Nonnegative Matrix Tri-Factorization (NMTF), factorization objective techniques, constrained NMF, and algorithmic improvements. We go over how NMF can be used in a variety of contexts, evaluate its effectiveness, and take into account how constraints can improve clustering quality.