This presentation explores the field-road diffusion model developed in 2012 by Berestycki, Roquejoffre, and Rossi. This parabolic system aims to capture the significant dispersal effects induced by lines of fast diffusion, with wide-ranging applications in population dynamics, ecology, and epidemiology. Initially, we will introduce the model, emphasizing its ability to simulate accelerated spread phenomena. Subsequently, we will discuss the derivation of its governing equations from an interacting particle system, thus providing a stochastic foundation for the deterministic model. Lastly, we will concentrate on the explicit determination of the fundamental solution to the macroscopic model, achieved through the application of a double integral transform, namely Fourier and Laplace. This analytical framework offers clear insights into the model's dynamics and sets the stage for exploring non-linear issues such as "persistence vs. extinction" phenomena in the presence of reaction terms with the so-called Allee effect