Basic composite properties can be related to those of their constituents by available theoretical results which are, on the one hand, relatively simple, and yet which are representative of the actual physical response of the materials. The present paper reviews recent developments in the theoretical analysis of the mechanical and thermal properties of fibrous composites. Comparisons with available experimental results are presented. Attention is focused on the properties of unidirectional fibrous composites. The definition of effective composite properties and methods for the analysis of the elastic moduli of such composites are reviewed. Theoretical results for composite thermal expansion coefficients and specific heats are presented. Tensile strength studies based on statistical failure models are then described. Effects of variations in fibre strength and of non-uniform stress distributions are treated. Finite length fibres and uniform strength fibres are also considered. Emphasis is placed upon demonstrating that the influence upon composite strength of the statistical nature of the strength of contemporary advanced filaments is susceptible to rational analysis.