Masonry is a composite material that can be defined as a material incorporating a visible internal structure and having a low strength in tension. The latter characteristic has shaped most civil engineering structures up to the advent of reinforced concrete and iron/steel. Masonry is also present in most of our cultural heritage buildings, which are part of our identity and represent a key attractor for tourism, a major economical asset of Europe with 10% of the GDP. The paper will address different challenges: micro-modelling and homogenization techniques, which represent both a popular and active field on masonry research; dynamics and earthquake engineering, which remain far from being understood and challenge our modelling capacities. The presentation also addresses dynamic identification and inverse problems, or the art of a modelling engineer, as well as the engineering use of sophisticated numerical models, which provide significance to most of the problems addressed before.