A rather natural “Lagrangian particle” discretisation of a 1d scalar conservation law leads to the so-called “Follow the Leader” approximation of it. While this has been formally known for many decades (see e.g. the 1974 book by Whitham), the first rigorous results came only in the past ten years. It is by know quite well known that a suitable “upwind” version of the FtL approximation converges (as the number of particles goes to infinity and through a suitable reconstruction of the Eulerian density) to the unique entropy solution to the corresponding conservation law in Kruzkov’s sense. We will review the main results in the literature, including a series of paper in collaboration with M. Rosini, S. Fagioli, and G. Russo, a set of results by Holden and Risebro, and a very recent result by Storbugt. Recurring strategies to prove compactness of the scheme include BV estimates and (more recently) compensated compactness. An alternative approach tries to catch the L1 to L infinity “smoothing effect” of the PDE through a discrete one-sided Lipschitz condition. We will describe the latter approach in more detail, based on a paper in collaboration with G. Stivaletta (2022). We will also address some possible extension of the whole theory and list some open problems.