Bayesian optimization uses a probabilistic model of the objective function to guide the search for the optimum. It is particularly interesting for the optimization of expensive-to-evaluate functions. For the last decade, it has been increasingly used for industrial optimization problems and especially for numerical design involving complex computer simulations. We feel that Bayesian optimization should be considered with attention by anyone who has to identify the parameters of a model based on a very limited number of model simulations because of model complexity. In this paper, we wish to describe, as simply as possible, how Bayesian optimization can be used in parameter identification and to present a new application. We concentrate on two algorithms, namely EGO (for Efficient Global Optimization) and IAGO (for Informational Approach to Global Optimization), and describe how they can be used for parameter identification when the budget for evaluating the cost function is severely limited. Some open questions that must be addressed for theoretical and practical reasons are indicated.