The paper discusses intrinsic random functions (IRFs), a generalization of stationary random functions (SRFs), used to model non-stationary phenomena. IRFs are defined as random functions with generalized covariances (GCs) that are conditionally positive definite. They allow for statistical inference from a single realization and are used in applications such as contouring and estimating problems. The paper introduces the concept of IRFs as a broader class than SRFs, with properties that make them suitable for modeling non-stationary data. It also discusses the best linear intrinsic estimator (BLIE), a method for estimating IRFs, and the turning bands method for simulating IRFs. The paper further explores polynomial GCs, which are useful for statistical inference through automatic procedures. The paper also presents a decomposition theorem showing that any continuous k-IRF can be expressed as the sum of a SRF and an infinitely differentiable k-IRF. It concludes with a discussion of the drift of IRFs and the conditions under which they are without drift. The paper also provides examples of IRFs and their applications, including the use of polynomial GCs in modeling non-stationary phenomena.The paper discusses intrinsic random functions (IRFs), a generalization of stationary random functions (SRFs), used to model non-stationary phenomena. IRFs are defined as random functions with generalized covariances (GCs) that are conditionally positive definite. They allow for statistical inference from a single realization and are used in applications such as contouring and estimating problems. The paper introduces the concept of IRFs as a broader class than SRFs, with properties that make them suitable for modeling non-stationary data. It also discusses the best linear intrinsic estimator (BLIE), a method for estimating IRFs, and the turning bands method for simulating IRFs. The paper further explores polynomial GCs, which are useful for statistical inference through automatic procedures. The paper also presents a decomposition theorem showing that any continuous k-IRF can be expressed as the sum of a SRF and an infinitely differentiable k-IRF. It concludes with a discussion of the drift of IRFs and the conditions under which they are without drift. The paper also provides examples of IRFs and their applications, including the use of polynomial GCs in modeling non-stationary phenomena.