This thesis is concerned with the application of complete search optimization methods to solve parameter estimation problems, with a focus on models taking the form of ordinary differential equations (ODEs). Complete search methods are of paramount importance in solving chemical and process systems engineering optimization problems, where multiple local optima are exhibited almost pathologically due to the frequent presence of highly nonlinear models. Meanwhile, parameter estimation problems are most commonly cast as an optimization exercise, where parameters are chosen such that model predictions match recorded observations as closely as possible. As such, the guarantee of global optimality should be considered a requirement in any model identifcation framework, particularly when observations are uncertain and further optimization problems must be solved to determine a region where parameter values are expected to lie. This thesis presents a new approach to nonlinear regression, called {\em set-membership nonlinear regression} (SMR). The SMR region is defined as the set of all global optimizers to a nonlinear regression problem in the presence of bounded uncertainty on the observed variables, and we show how to enclose this region for both algebraic-input and dynamic models by solving a set of semi-infinite optimization problems. In addition, this thesis presents an extension of set-valued integration to enable efficient sensitivity analysis of parameter-dependent ODE systems, using both the forward and adjoint methods. Auxiliary ODE systems are derived whose solutions define bounds on the forward and adjoint sensitivity trajectories. These methods are further used in solving global dynamic optimzation problems, where optimality conditions are used as redundant constraints in order to reduce the search space. Efficient numerical implementation is at the forefront of all research described in this thesis. All methods described can be found within the library CRONOS https://github.com/omega-icl/cronos}, which makes use of the library MC++ https://github.com/omega-icl/mcpp.