This book introduces the underlying concepts of column dynamics and buckling, based on the latest state-of-the-art research on this innovative topic. It begins with a summary of the basic concepts behind column dynamics and buckling, before moving on to the models for studying dynamic buckling inside oil wells. Four models with increasing complexity are presented: columns without friction; columns with friction; columns inside slant wells; and columns inside offshore wells. Each model is divided into two cases, depending on whether the column is being tripped in or out. A case study is used to demonstrate these models and is further developed as each model is presented and explained. The results include comparisons between the models themselves, thus showing the implications of the adopted hypotheses of each. This book enables academic, industrial, and graduate student readers to fully understand the fundamentals of dynamic buckling and to further develop the presented models for their own research.