Topological states of matter have been intensively studied in crystals, leading to fascinating phenomena such as scattering-free edge current in topological insulators. However, the power of topological protection goes well beyond ordered crystal lattices. In this talk we explore how topology protects mechanical edge modes in messy, noncrystalline, systems. We will use disordered fiber networks and quasicrystals as our examples, to demonstrate how topological edge floppy modes can be induced in these structures by controlling their geometry. Fiber networks are ubiquitous in nature and especially important in bio-related materials. Quasicrystals show unusual orientational order with quasiperiodic translational order. Realizing topological edge floppy modes in these noncrystalline structures may open the door to rich new physics in biological networks as well as novel designs of topological mechanical metamaterials.