This dissertation studies the dynamics of political competition from an outsider's perspective across contemporary democracies. Due to differences in the initial conditions of competition, not all political parties possess the same resources nor can they all follow the same strategies to obtain votes. Outsider political parties are those who are neither in executive government nor traditional opposition parties but, rather, they are clearly excluded from mainstream politics because they fail to fall neatly within the Left-Right political continuum. In order to break into their party system and gain power, some outsider parties choose radicalism as a strategy of entry and of persuasion. To become radical, outsider parties introduce a new, neglected or forgotten issue dimension into the political arena and with it, they question the validity of the entire establishment. Thus, radicalism allows outsiders to differentiate themselves from all other actors, to challenge the terms in which politics takes place and, ideally, to reshape their particular political system in order to abandon their condition of permanent losers. I first describe and explain my theory of radicalism. I dispute the conventional wisdom which defines it as an extremist or fundamentalist, ideological choice and present radicalism as an instrumental tactic dependent on the actual nature of the establishment and the specific moment in which such strategic choice was made. I then rely on two different expert surveys to empirically distinguish amongst the established, the outsider and the radical parties and continue to compare and contrast them in a cross-sectional study of 30 liberal democracies and 247 political parties. Finally, I trace the particular evolution -- through time and space-- of the radical strategy in four case studies in two Western European countries and two Latin American. My findings reveal first that radicalism is, indeed, a strategy available only for outsider parties. Second, that it is a response to a rigid party system. Third, that it relies on a trial and error process for selecting the "right" issue dimension and that such a selection process is endogenous and party-leadership driven