During the last decade, the field of metasurfaces has drawn significant attention due to the unprecedented control over the optical properties of light in a very short propagation distance with high resolution. These devices consist of nanostructures defined within a single layer of metal or dielectric materials. Recently, several optimization methodologies including both local and global search methods have been considered to tune the parameters of these nanostructures according to the desired applications. The former, require fewer iterations, however, they can be stuck in local maxima/minima, the later is more general and converges to the global solution. Nevertheless, most of the global techniques used so far require costly simulations, which make them inapplicable for modelling 3D real-life designs. In this contribution, we present an efficient global optimization method that belongs to the class of Bayesian optimization and is known as Efficient Global Optimization (EGO) to optimize highly efficient metasurface designs. We will discuss both single and multiobjective optimization problems and demonstrate numerically the ability of the EGO in obtaining the global solution using a few numbers of solver calls even in the case of large parameter space with multiple objectives. Various optimized real-life applications will be considered ranging from beam deflectors and achromatic large-scale metalenses.