Three grades of catalytically grown and chemical vapor deposited Pyrograf®-III carbon nanofibers with an average diameter of 150 nm were tested individually for their tensile strength. Preliminary experiments by a novel MEMS-based mechanical testing platform were performed to characterize the interfacial adhesion of these nanostructures to EPON epoxy commonly used in aerospace applications. The nominal tensile strengths of the nanofibers followed Weibull distributions varying between 2-5 GPa. These are the first strength measurements of individual carbon nanofibers, which, to date, were assumed to have a strength of 7 GPa, or that of larger scale carbon fibers in laminated composites. The nanofiber fracture surface geometry agreed well with the stacked "Dixie-cup" structure of oblique graphene layers comprising the nanofibers. High resolution images of fractured nanofibers indicated the potential slip between neighboring graphene layers with respect to each other as a frequent failure mechanism under uniaxial tension. The pull-out experiments showed a non-linear correlation between the pull-out force and displacement and revealed significant frictional component during nanofiber pull-out.