H. Masur showed in the early 80s that almost every Teichmüller ray converges to a unique point in PMF. It is also known since a while that there are rays that have more than one accumulation point in the boundary.

I will give an overview of what is understood so far about the limit sets of Teichmüller rays, mentioning some recent progress. For example, I will mention recent joint work with K. Rafi and B. Modami where we give a construction of a ray whose limit set in PMF is a d-dimensional simplex.