MDS matrices allow to build optimal diffusion layers in the design of block ciphers and hash functions. A recursive MDS matrix is an MDS matrix which can be expressed as a power of some companion matrix. The advantage of such a matrix is that it can be implemented by a single LFSR clocking several times. Such matrices are suitable for the design of a diffusion layer in light-weight cryptographic applications. In this talk, we will discuss some constructions of recursive MDS matrices.