In "Information Retrieval", relevance is a numerical score assigned to a search result, representing how well the results meet the information need of the user that issued the search query. In many cases, a result's relevance determines the order in which it is presented to the user. In this thesis we have explored the information retrieval models in general and relevancy ranking within information retrieval in particular. Several mathematical tools have been used in research for improving the relevancy ranking models. A simple yet useful type of relevancy models are based on viewing each document and each query as elements in a high dimensional vector space, and using the angle between the document and the query as a measure of similarity. More advanced concepts in linear algebra, such as the Singular Value Decomposition, and theory of Markov chains have also been employed for innovating relevancy ranking. Some of researches have also suggested and which is also true to certain extent that probability theoretic based models, such as inference and neural networks are the best theoretical foundation for relevancy ranking models. A particularly important question is how to assess the "goodness" of a relevancy model. There is also a greater need to focus on eff ective and optimized implementations, such as query latency times should be in the sub-second domain. Theoretically \recall" and \precision" are used as measures for analyzing the effectiveness of a relevancy ranking models. But with the advent of new and sophisticated models there is a need to have a better framework for evaluation.