Thin-ply composite materials display remarkable versatility and hold great promise for applications in the space industry. They are characterized by exceptional attributes such as a high strength-to-weight ratio, fatigue resistance, and the ability to conform to high curvatures without failure. This study investigates the behavior of thin-ply composite materials and structures, with a particular emphasis on their relevance to deployable space applications. Deployable structures such as solar sails, are large structures that are designed to be compactly folded into small volumes to fit inside the spacecraft for the purpose of carrying them to space. These structures utilize the strain energy during folding, to facilitate the deployment sequence and attain the intended original configuration of the structure. However, the viscoelastic nature of the composite material leads to a reduction of strain energy over the storage period, leading to shape inaccuracies after deployment. Our research includes an in-depth analysis of the viscoelastic properties of the composite material and the behavior of structures following folding and subsequent deployment. The viscoelastic mechanical properties of the materials were assessed through a numerical multi-scale homogenization approach. We examined thin-ply laminates with varying orientations and ply arrangements and conducted experimental studies to validate the numerical models. We subsequently incorporated the viscoelastic properties of the laminates into the simulation of deployable structures. The laminate properties were evaluated both at the ply level and at the laminate level. Numerical simulations were conducted to study the behavior of a composite boom during folding, stowage, deployment, and subsequent shape recovery. Our research extended to characterizing the composite material based on available test data, as well as examining the stowage and recovery behavior of a structure constructed from unidirectional composites.