Technological progress, such as robotics and artificial intelligence, is often blamed for the loss of jobs and rising income inequality. It is also linked to increasing inequality in the corporate landscape as superstar firms forge ahead in winner-takes-most markets. Our analysis shows that in most sectors there is a high degree of concentration among a few top companies in research and development spending. R&D spending is much more concentrated than sales and employment. In 2015, for example, the top 10 percent biggest spenders on R&D, accounted for 71 percent of the R&D spending of the 2500 companies that spend most on R&D. This concentration is most obvious in the high-tech biopharma and digital sectors, though it is also true for other sectors, such as the vehicles sector. US companies are overrepresented among these R&D superstars, especially in digital sectors where they take up half of the top slots. Over the last decade, there has been little evidence for increasing concentration in the global R&D landscape. On the contrary, a slight decline is discernible. Slight increasing concentration can only be detected in digital sectors, with in particular the top 1 percent of R&D spending firms in these sectors forging ahead. Although the overall concentration of R&D spending among a few leading firms might not be changing much over time, R&D leaders are slowly losing their positions to new R&D-leading firms. Digital Services is the most turbulent high-tech sector. The US and China are more likely to produce new R&D leaders that take over some of the top positions from incumbent R&D leaders. This poses difficult questions for Europe, which is at risk of losing out in terms of R&D leadership in more technologically advanced sectors.