In recent times, a clear trend towards the use of biobased materials can be seen in many areas. Apart from beneficial ecological properties, high strength and stiffness at low weight are desirable in structural applications, a combination typically offered by cellulose-based materials. As an adaption to mechanical stresses acting on the living organism, most biobased fibre materials inherently show anisotropic mechanical properties and feature a preferred orientation of high-strength cellulose fibres. In both nature and engineering, unidirectional fibre orientation might be beneficial since only this arrangement fully exploits the high strength and stiffness of the cellulose biopolymer. The present paper is a selective review of cellulose-based fibre materials with either unidirectional or close-to unidirectional orientation. This includes, amongst others, materials derived from wood or bamboo, natural fibre composites, all-cellulose composites and nanocellulose-based materials. This review shall serve as an indicator of the strength potential inherent to biobased cellulosic materials in order to ascertain their suitability for potential applications. Each type of material is described in terms of structure and corresponding representative values for strength and modulus of elasticity in fibre direction. Finally, a concise comparison of individual fibre and bulk materials in terms of mechanical performance is provided.