Many exotic materials properties arise in defect-free crystals. Examples include single-walled carbon nanotubes and graphene whose sp2 bonded carbon networks lead to extreme strength, conductivity, and carrier mobility. A defect in an otherwise perfect nanocrystal, however, introduces a singularity where new chemistry and physics may emerge. Over the last few years, experimental tools and theoretical approaches have emerged to study electron scattering, phonon coupling, excitons diffusion and trapping, and spin-orbital coupling at chemically tailored defect sites on nanocarbons and several other low dimensional materials. This TSRC workshop expands on our successful 2013 workshop focusing on carbon nanotubes and attempts to bring together researchers at this new frontier to discuss current challenges and opportunities from chemical, physical, and theoretical perspectives. The scope will range from defect creation by organic chemistry and physical means, to defect characterization with scanning probes, single molecule spectroscopy and electrical transport, to theoretical predictions based on molecular dynamics and quantum mechanics.