Increasing parameter variations, high defect densities and a growing susceptibility to external noise in nanoscale technologies have led to a paradigm shift in design. Classical design strategies based on worst-case or average assumptions have been replaced by statistical design, and new robust and variation tolerant architectures have been developed. At the same time testing has become extremely challenging, as parameter variations may lead to an unacceptable behavior or change the impact of defects. Furthermore, for robust designs a precise quality assessment is required particularly showing the remaining robustness in the presence of manufacturing defects. The paper pinpoints the key challenges for testing nanoelectronic circuits in more detail, covering the range of variation-aware fault modeling via methods for statiscal testing and their algorithmic foundations to robustness analysis and quality binning