Precision medicine or personalized medicine has been proposed as a modernized and promising medical strategy. Genetic variants of patients are the key information for implementation of precision medicine. Next-generation sequencing (NGS) is an emerging technology for deciphering genetic variants. Alignment of raw reads to a reference genome is one of the key steps in NGS data analysis. Many algorithms have been developed for alignment of short read sequences since 2008. Users have to make a decision on which alignment algorithm to use in their studies. Selection of the right alignment algorithm determines not only the alignment algorithm but also the set of suitable parameters to be used by the algorithm. Understanding these algorithms helps in selecting the appropriate alignment algorithm for different applications in precision medicine. Here, we review current available algorithms and their major strategies such as seed-and-extend and q-gram filter. We also discuss the challenges in current alignment algorithms, including alignment in multiple repeated regions, long reads alignment and alignment facilitated with known genetic variants.