In contemporary Europe, far-right parties threaten liberal democratic principles such as pluralism, media freedom and minority rights. Despite the stigma they normally face, far-right parties have experienced electoral breakthroughs even in countries where they remained electorally marginal such as Germany, Portugal, Spain and Sweden. We advance the idea that this happened because the level of stigmatization faced by these parties decreased before their electoral breakthrough. Therefore, we form a theoretical framework based on a threefold mechanism: far-right parties manage to reduce the stigma they face because of a reputational shield or by moderating their message; the media help the far right gain visibility and legitimacy by accommodating its views; established parties accommodate far-right parties without ostracizing them. Then, we test the framework by looking at the electoral breakthroughs of four parties: the results confirm the expectations except for the role of established parties, which is inconclusive.