The estimation and compensation of processes with time delays have been of interest to academics and practitioners for several decades. A full review of the literature for both model parameter and time delay estimation is presented. Gradient methods of parameter estimation, in open loop, in the time and frequency domains are subsequently considered in detail. Firstly, an algorithm is developed, using an appropriate gradient algorithm, for the estimation of all the parameters of an appropriate process model with time delay, in open loop, in the time domain. The convergence of the model parameters to the process parameters is considered analytically and in simulation. The estimation of the process parameters in the frequency domain is also addressed, with analytical procedures being defined to provide initial estimates of the model parameters, and a gradient algorithm being used to refine these estimates to attain the global minimum of the cost function that is optimised. The focus of the thesis is subsequently broadened with the consideration of compensation methods for processes with time delays. These methods are reviewed in a comprehensive manner, and the design of a modified Smith predictor, which facilitates a better regulator response than does the Smith predictor, is considered in detail. Gradient algorithms are subsequently developed for the estimation of process parameters (including time delay) in closed loop, in the Smith predictor and modified Smith predictor structures, in the time domain; the convergence of the model parameters to the process parameters is considered analytically and in simulation. The thesis concludes with an overview of the methods developed, and projections regarding future developments in the topics under consideration.