Multiple‐point geostatistics is a general statistical framework to model spatial fields displaying a wide range of complex structures. In particular, it allows controlling connectivity patterns that have a critical importance for groundwater flow and transport problems. This approach involves considering data events (spatial arrangements of values) derived from a training image (TI). All data events found in the TI are usually stored in a database, which is used to retrieve conditional probabilities for the simulation. Instead, we propose to sample directly the training image for a given data event, making the database unnecessary. Our method is statistically equivalent to previous implementations, but in addition it allows extending the application of multiple‐point geostatistics to continuous variables and to multivariate problems. The method can be used for the simulation of geological heterogeneity, accounting or not for indirect observations such as geophysics. We show its applicability in the presence of complex features, nonlinear relationships between variables, and with various cases of nonstationarity. Computationally, it is fast, easy to parallelize, parsimonious in memory needs, and straightforward to implement.

River‐groundwater interactions are at the core of a wide range of major contemporary challenges, including the provision of high‐quality drinking water in sufficient quantities, the loss of biodiversity in river ecosystems, or the management of environmental flow regimes. This paper reviews state of the art approaches in characterizing and modeling river and groundwater interactions. Our review covers a wide range of approaches, including remote sensing to characterize the streambed, emerging methods to measure exchange fluxes between rivers and groundwater, and developments in several disciplines relevant to the river‐groundwater interface. We discuss approaches for automated calibration, and real‐time modeling, which improve the simulation and understanding of river‐groundwater interactions. Although the integration of these various approaches and disciplines is advancing, major research gaps remain to be filled to allow more complete and quantitative integration across disciplines. New possibilities for generating realistic distributions of streambed properties, in combination with more data and novel data types, have great potential to improve our understanding and predictive capabilities for river‐groundwater systems, especially in combination with the integrated simulation of the river and groundwater flow as well as calibration methods. Understanding the implications of different data types and resolution, the development of highly instrumented field sites, ongoing model development, and the ultimate integration of models and data are important future research areas. These developments are required to expand our current understanding to do justice to the complexity of natural systems.