Traditionally, Armenia has had a leading position within the computer science and Information Technology sectors in the South Caucasus region and beyond. Information Technology (IT) is also one of the fastest growing industries of the Armenian economy [1]. In 2000, the Government of Armenia recognized the IT sector as the primary constituent of the country's economic progress. Armenia is, more than ever, in need of cutting-edge and relevant e-infrastructures and e-services to tackle today's societal and scientific challenges. The Institute for Informatics and Automation Problems (IIAP) of the National Academy of Sciences of the Republic of Armenia (NAS RA) [2] is the only state supported structure for software, hardware, and brainware technologies in Armenia. The institute is responsible for Armenia's National research and education network (Academic Scientific Research Computer Network of Armenia, ASNET-AM) [3] and the National Grid Initiative (ArmNGI) [4], and provides computational and networking facilities and advanced services to users. The main objective of this article is to highlight key activities that will spur Armenia to strengthen its scientific computing capacity thanks to the analysis made of the current trends of e-Infrastructures in Europe and the USA.