The background to numerical modeling was introduced in-line with the concept of this book. The focus of this chapter is to introduce readers to the role of mathematics in furthering environmental research. Salient concepts of numerical methods were discussed with its peculiar pros and cons. Each of the highlighted numerical methods was elaborated with worked examples. The applications of numerical methods in environmental modeling were discussed with examples. Also, insightful counsels for beginner in the field were emphasized to guide against erroneous concept in applying numerical methods in environmental modeling.