There has been a deluge of biological sequence data in the public domain, which makes sequence comparison one of the most fundamental computational problems in bioinformatics. The biologists routinely use pairwise alignment programs to identify similar, or more specifically, related sequences (having common ancestor). It is a well-known fact that almost everything in bioinformatics depends on the inter-relationship between sequence, structure, and function (all encapsulated in the term relatedness), which is far from being well understood. The potential relatedness of two sequences is better judged by statistical significance of the alignment score rather than by the alignment score alone. This chapter presents a summary of recent advances in accurately estimating statistical significance of pairwise local alignment for the purpose of identifying related sequences, by making the sequence comparison process more sequence specific. Comparison of using pairwise statistical significance to rank database sequences, with well-known database search programs like BLAST, PSI-BLAST, and SSEARCH, is also presented. As expected, the sequence-comparison performance (evaluated in terms of retrieval accuracy) improves significantly as the sequence comparison process is made more and more sequence specific. Shortcomings of currently used approaches and some potentially useful directions for future work are also presented.