Delay test in nano-scale VLSI circuits becomes more difficult with shrinking technology feature sizes and rising clock frequencies. In this dissertation, we study three challenging issues in delay test: fault modeling, variational delay evaluation and path selection under process variation. Previous research of fault modeling on resistive spot defects, such as resistive opens and bridges in the interconnect, and resistive shorts in devices, lacked an accurate fault model. As a result it was difficult to perform fault simulation and select the best vectors. Conventional methods to compute variational delay under process variation are either slow or inaccurate. On the problem of path selection under process variation, previous approaches either choose too many paths, or missed the path that is necessary to be tested. We present new solutions in this dissertation. A new fault model that clearly and comprehensively expresses the relationship between electrical behaviors and resistive spots is proposed. Then the effect of process variations on path delays is modeled with a linear function and a fast method to compute coefficients of the linear function is also derived. Finally, we present the new path pruning algorithms that efficiently prune unimportant paths for test, and as a result we select as few as possible paths for test while the fault coverage is satisfied. The experimental results show that the new solutions are efficient and accurate.