In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived from calculus, but can be suitably modified to solve more complex problems; and finally provide pointers on how to train students through the UR process that can help to impact student's future academic and non-academic careers.