The theory of optimal design of experiments is implemented in two different ways: either a continuous optimal design is found using continuous optimization methods, in which only the proportions of runs made at each support point are found and the continuous design is then rounded to obtain a design for the experiment, or an exact near-optimal design is found using discrete optimization methods, which can only be guaranteed to converge to local optima, but give a design for the experiment directly. Continuous designs are usually more useful when the number of runs in the experiment is much greater than the number of parameters in the model, especially for nonlinear models. On the other hand, exact designs are usually more useful for experiments with multiple factors, in which the number of runs is typically not much greater than the number of parameters, especially in linear models. Recently there has been increasing interest in nonlinear models with multiple factors, which are often hybrids of mechanistic and empirical models. In such cases continuous designs can be unsatisfactory, without the rounding becoming a new search in itself, while exact design methods suffer from the need to specify a discrete set of candidate points. Some new exact design algorithms will be discussed which try to get round these problems. They include using algebraic expressions for the optimality criterion, using the continuous design to suggest candidate points and using continuous multidimensional optimization to avoid the need for candidate points.