Geostatistical simulation is used in uncertainty quantification and management in many fields of Earth Sciences. Conventional tools account only for two-points statistics and are unable to capture complex features. Multiple-point statistics (MPS) simulations provide improved flexibility to reproduce complex features and can be used for categorical and continuous variables, or even in a multivariate context, but these methods also bring new challenges in regards to inference, computational implementation and validation. In this paper, we review the methods and tools necessary to implement and use MPS methods. The place of multiple-point simulation is discussed and a review of the building blocks required to implement a MPS method are presented. We describe the main methods and discuss some of the assumptions, challenges and limitations of these methods. MPS simulation expands the toolkit of earth scientists and may be key to assess transfer functions that are dependent on specific connectivity patterns.