New approaches to the role of innovation activities in the context of contemporary challenges of economic growth, as well as the needs and possibilities to improve the assessment and modelling of the impact of investment into the research and development (R&D) on economic growth are presented in this publication. The main attention is focused on the processes of innovation activities and economic growth in the European Union, as well as on the goals that are formulated in the Strategy “Europe 2020” and in other documents of the European Union. The peculiarities of the application of various indicators and indices are disclosed, in particular, taking into account the needs for developing and substantiating economic policy decisions. New aspects of the application of various innovation indexes, such as Global Innovation Index, EU Innovation Scoreboard, Competitive Industrial Performance Index, Global Competitiveness Index, Knowledge Economy Index and Innovation Capacity Index, are presented. A new method of the assessment and modelling of the impact of the investment into the R & D on economic growth is proposed and described.