The term Berry?s random wave describes a canonical model for a Gaussian Laplace eigenfunction on the plane. This universal object naturally arises in connection with several questions in stochastic geometry, especially those concerning the local behaviour of Laplace eigenfunctions?random or deterministic?on chaotic surfaces. After a brief introduction to this model, I will highlight two striking (and still quite mysterious) structures that emerge in high-frequency regimes: * Randomly scattered scars * Total disorder processes (if time permits) The second part of the talk will mainly focus on open problems and conjectures, and will include some personal reflections and anecdotes about doing mathematical research in the era of AI.