Over the last three decades, numerous radical right populist parties (RRPP) have emerged, developed, and strengthened their electoral weight in Western Europe. Yet, while several RRPP have managed to formally participate in government coalitions (such as in Italy, Austria, and Switzerland) or to informally support minority governments (such as in Denmark, and in The Netherlands) and while other RRPP have become highly visible opposition forces (such as in France, and Germany), the influence exercised by RRPP remain underexplored. It is essential to focus on their policy influence because of their electoral strength but also because they are often perceived by journalists, citizens, policy-makers as well as by researchers as a threat to democracy. As a reaction, mainstream parties tend to adopt specific strategies - such as measures of militant democracy towards RRPP.