Clarifying the historic relationship between Responsible Innovation (RI) and Technology Assessment (TA) can benefit both fields. To achieve this, a basic distinction is made between TA directed toward the promotion side of technology (Constructive Technology Assessment [CTA]) and the control side (Parliamentary TA). In particular, CTA can be seen as a major source of the idea of framing innovation policy in terms of transformative innovation and RI. Originally, the practice of CTA was directed toward democratizing the promotion side of technology. The practice of RI has the broader ambition of encompassing both the promotion and the control side of technology. Parliamentary TA’s familiarity with the control side of technology could inspire RI. At the same time, RI challenges Parliamentary TA to pay more attention to the promotion side of technology and to stimulating politically desired effects of innovation. Accordingly, the paper describes three challenges faced by both TA and RI: representation, issue identification, and directionality. Since Parliamentary TA and RI can inspire each other in many ways, a more intensive interaction between CTA/RI practitioners and Parliamentary/RI practitioners is both desirable and necessary.