Through years of evolution, biological soft fibrous tissues have developed remarkable functional properties, unique hierarchical architectures, and -most notably, an unparalleled and extremely efficient deformation ability. Whereas the structure-function relationship is well-studied in natural hard materials, soft materials are not getting similar attention, despite their high prevalence in nature. These soft materials are usually constructed as fiber-reinforced composites consisting of diverse structural motifs that result in an overall unique mechanical behavior with large deformations. Biomimetics of their mechanical behavior is currently a significant bioengineering challenge. The unique properties of soft fibrous tissues stem from their structural complexity, which, unfortunately, also hinders our ability to generate adequate synthetic analogs, such that autografts remain the “gold standard” materials for soft-tissue repair and replacement. This review seeks to understand the structural and deformation mechanisms of soft collagenous tissues, with a particular emphasis on tendon and ligaments, the annulus fibrosus (AF) in the intervertebral disc (IVD), skin, and blood vessels. We examined and compared different mechanical and structural motifs in these different tissue types, which are subjected to complex and varied mechanical loads, to isolate the mechanisms of their deformation behavior. Herein, we focused on their composite structure from a perspective of the different building blocks, architecture, crimping patterns, fiber orientation, organization and their structure-function relationship. In the second part of the review, we presented engineered soft composite applications that used these structural motifs to mimic the structural and mechanical behavior of soft fibrous tissues. Moreover, we demonstrated new methodologies and materials that use biomimetic principles as a guide. These novel architectural materials have tailor-designed J-shaped large deformations behavior. Structural motifs in soft composites hold valuable insights that could be exploited to generate the next generation of materials. They actually have a two-fold effect: 1) to get a better understanding of the complex structure-function relationship in a simple material system using reverse biomimetics and 2) to develop new and efficient materials. These materials could revolutionize the future tailor-designed soft composite materials together with various soft-tissue repair and replacement applications that will be mechanically biocompatible with the full range of native tissue behaviors.