Ameshref: a Matlab-toolbox for adaptive mesh refinement in two dimensions. This paper presents a Matlab-Toolbox named ameshref that provides an efficient implementation of various adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes. For selected methods, we give an insight into the strategy itself and the core ideas for an efficient realization. This is achieved by utilization of reasonable data structure, use of Matlab built-in functions and vectorization. To serve educational purposes on how to implement a method efficiently, the code is kept accessible but short. Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use. Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education.