This chapter focuses on modeling chemical reactions—Jacobian paradigm and related issues. Being perfect for linear equations, Jacobian-based methods have been adapted to the nonlinear case with considerable success. It sometimes seems as if Jacobians yield a general solution paradigm: if the equations are linear, solve the set of equations once; and if the equations are nonlinear, solve the set of equations repeatedly—iterate—until the process converges. Linear equations are defined as equations in which the parameters appear only as first power multipliers of terms containing no other parameters. Nonlinear models arise primarily because they are implied by scientific assumptions, for example, by the laws of mass action. Because the definition of a nonlinear model is any model that is not linear, the variety of such models is considerable. The chapter explores the iterative process in three contexts: (1) curve fitting, (2) rate equations, and (3) equilibrium or steady-state equations. The chapter also examines how all three of these contexts can coexist, using a problem in enzyme kinetics.