In this seminar we will talk about how to simulate quantum physical models via discrete-time quantum walks (DTQWs) over hexagonal and triangular lattices. We will define what a QW is from a computer science perspective. The study of QWs is growing due to two reasons. First, different kind of Quantum Computing algorithms have been created using them in an efficient way. On the other hand, they can be used for the purpose of quantum simulating in the future quantum simulation devices. From the quantum simulation perspective, QWs have been extensively used for reproducing relativistic particles dynamics described by the Dirac equation, always using regular lattices. We will show that QWs does not need to rely on the regular lattice grid, and that they can be casted on the hexagonal and triangular grid instead. We believe that this constitutes an important step towards: modeling propagation in crystalline materials; identifying substrates for QW implementations; studying topological phases and understanding propagation in discretized curved spacetime.