  We provide an overview of the results on Hughes' model for pedestrian
movements available in the literature.
  After the first successful approaches to solving a regularised version of the
model, researchers focused on the structure of the Riemann problem, which led
to local-in-time existence results for Riemann-type data and paved the way for
a WFT (Wave-Front Tracking) approach to the solution semigroup. In parallel, a
DPA (Deterministic Particles Approximation) approach was developed in the
spirit of follow-the-leader approximation results for scalar conservation laws.
Beyond having proved to be powerful analytical tools, the WFT and the DPA
approaches also led to interesting numerical results.
  However, only existence theorems on very specific classes of initial data
(essentially ruling out non-classical shocks) have been available until very
recently. A proper existence result using a DPA approach was proven not long
ago in the case of a linear coupling with the density in the eikonal equation.
Shortly after, a similar result was proven via a fixed point approach.
  We provide a detailed statement of the aforementioned results and sketch the
main proofs. We also provide a brief overview of results that are related to
Hughes' model, such as the derivation of a dynamic version of the model via a
mean-field game strategy, an alternative optimal control approach, and a
localized version of the model. We also present the main numerical results
within the WFT and DPA frameworks.
