Theoretical results for electron transport through two structures involving carbon nanotubes are presented. The first structure was a nanotube inserted into another nanotube of a larger diameter. The electrical conductance of the resulting double-wall CNT is an oscillatory function of the length of the insertion. The frequency and amplitude of these oscillations reflect the position dependence of inter-tube interaction in multi-wall CNTs. The second structure was a single-wall carbon nanotube (CNT) in contact with ferromagnetic electrodes, exhibiting giant magnetoresistance (GMR). An intuitive picture of GMR in clean nanotubes with low-resistance contacts is presented and ab initio results are obtained for GMR in Nickelcontacted nanotubes.