This chapter derives the calculation of functional determinants based on the definition of the determinants. It explains the particulars of the determinant calculation in the one-dimensional situation and provides some closed formulas for the determinant of second-order operators with potential. The chapter presents some known results using the contour integral techniques and considers the effect that the presence of zero modes has on the determinant. It considers the determinant associated with the coexact zeta function, which is simply a combination of Robin and Dirichlet contributions. Finally, the chapter presents an indirect method for the calculation of determinants based on its transformation properties under conformal variations.