In recent years, there have been a lot of new developments concerning the use of advanced materials for lightweight structures. Examples are long- and short-fibre-reinforced composites, sandwiches, foams, and, last but not least, nanostructures. The analysis of structures made of these materials can be performed on the basis of the Mechanics of Composites. However, stimulated by new applications, new manufacturing technologies, new material compositions, etc. a review of the Mechanics of Composites is necessary. In this article, some of the actual trends are discussed, for example developments in the application of long-and short-fibre-reinforced composites, laminates affected by multifield loadings, effective property-based analysis of foams, and the description of nanostructures within the concepts of Continuum Mechanics. The starting point of the review are the Engineering Mechanics basics on the level of the BSc program, that means the classical Strength of Materials. Extensions of Materials Strength foundations (for example, inclusion of anisotropy) are often sufficient as first improved estimates. If it is necessary, elements of Continuum Mechanics, of Material Testing or Numerical Solution Techniques can be implied. The every year increasing number of publications in the field of advanced materials for lightweight structures does not allow to give a complete overview over the state of the art. Recognizing this fact, the author will give a report only of directions related to his own research group and/or in the surrounding of his team.