Biological tissues represent fascinating dynamics leading to the formation of structures and patterns at larger scales compared to cell size. It is a big challenge to understand how cells communicate with each other to coordinate their dynamics and create orders. As an example, cells sort out into distinct populations, keeping a sharp straight interface between them. On the other side, cells can express polarities and the polarity field reveals long distance patterns. In this talk, I would like to present physical models to address some mechanisms that contribute to establishment of stable patterns. First, we will discuss how local interactions of cells at the interface influence its shape and mechanics. In the second case, I present a theoretical model to describe dynamics of polarity fields. Our model generalizes classical spin models by incorporating effective transport of polarity molecules between neighboring cells. We study how the intercellular transport qualitatively affects dynamics and leads to the formation of non-trivial patterns.