Bayesian Optimization (BO) methods are often used to optimize an unknown function f(���) that is costly to evaluate. They typically work in an iterative manner. In each iteration, given a set of observation points, BO algorithms select k ��� 1 points to be evaluated. The results of those points are then added to the set of observations and the procedure is repeated until a stopping criterion is met. The goal is to optimize the function f(���) with a small number of experiment evaluations. While this problem has been extensively studied, most existing approaches ignored some real world constraints frequently encountered in practical applications. In this thesis, we extend the BO framework in a number of important directions to incorporate some of these constraints. First, we introduce a constrained BO framework where instead of selecting a precise point at each iteration, we request a constrained experiment that is characterized by a hyper-rectangle in the input space. We introduce efficient sequential and non-sequential algorithms to select a set of constrained experiments that best optimize f(���) within a given budget. Second, we introduce one of the first attempts in batch BO where instead of selecting one experiment at each iteration, a set of k > 1 experiments is selected. This can significantly speedup the overall running time of BO. Third, we introduce scheduling algorithms for the BO framework when: 1) it is possible to run concurrent experiments; 2) the durations of experiments are stochastic, but with a known distribution; and 3) there is a limited number of experiments to run in a fixed amount of time. We propose both online and offline scheduling algorithms that effectively handle these constraints. Finally, we introduce a hybrid BO approach which switches between the sequential and batch mode. The proposed hybrid approach provides us with a substantial speedup against sequential policies without significant performance loss. / Graduation date: 2013