Tissue engineering offers a paradigm shift in the treatment of back pain. Engineered intervertebral discs could replace degenerated tissue and overcome the limitations of current treatments that disrupt the biomechanics of the spine. New materials, which exhibit sophisticated mechanical responses, are needed to provide templates for tissue regeneration. These behaviours include time-dependent deformation---facilitating shock absorption and nutrient transfer---and strong material anisotropy and tensile-compressive nonlinearities---providing flexibility in controlled directions. In this work, frameworks for the design of materials with controllable structure-property relationships are developed. The time-dependent mechanical properties of composites of agar, alginate and gelatin hydrogels are investigated. It is shown that the time-dependent responses of the composites can be tuned over a wide range. It is then demonstrated that materials mimicking the fibre-reinforced nature of natural tissues can be developed by infiltrating thick electrospun fibre networks with alginate. These fibre-reinforced hydrogels have tensile and compressive properties that can be separately altered. To better understand the mechanical behaviour of these hydrogel-based materials, improved methods for characterising poroelastic and poroviscoelastic time-dependent material properties using indentation are developed. It is shown that poroviscoelastic relaxation is the product of separate poroelastic and viscoelastic relaxation responses. The techniques developed here provide a methodology to rapidly characterise the properties of time-dependent materials and to create materials with complex structure-property relationships similar to those found in natural tissues; they present a framework for biomimetic materials design. The work in this thesis can be used to inform the design of clinically relevant tissue engineering treatments and help the quarter of a million people each year who undergo spinal surgery to reduce back pain.