The Mat\'ern model has been a cornerstone of spatial statistics for more than half a century. More recently, the Mat\'ern model has been central to disciplines as diverse as numerical analysis, approximation theory, computational statistics, machine learning, and probability theory. In this article we take a Mat\'ern-based journey across these disciplines. First, we reflect on the importance of the Mat\'ern model for estimation and prediction in spatial statistics, establishing also connections to other disciplines in which the Mat\'ern model has been influential. Then, we position the Mat\'ern model within the literature on big data and scalable computation: the SPDE approach, the Vecchia likelihood approximation, and recent applications in Bayesian computation are all discussed. Finally, we review recent devlopments, including flexible alternatives to the Mat\'ern model, whose performance we compare in terms of estimation, prediction, screening effect, computation, and Sobolev regularity properties.

翻译：马特恩模型作为空间统计学的基石已有半个多世纪的历史。近年来，该模型在数值分析、逼近理论、计算统计学、机器学习和概率论等多个学科领域占据核心地位。本文以马特恩模型为主线展开跨学科探索。首先，我们回顾马特恩模型在空间统计估计与预测中的重要性，并建立其与受该模型影响的其他学科的联系。随后，将马特恩模型置于大数据与可扩展计算的文献框架中：讨论SPDE方法、Vecchia似然近似及其在贝叶斯计算中的最新应用。最后，我们综述最新进展，包括马特恩模型的柔性替代方案，并从估计、预测、屏蔽效应、计算效率和Sobolev正则性属性等方面比较其性能。