The biggest fear most have of libertarianism is the rise of Government-like entities coming into power. But the kind of libertarianism most koch types have is this fake private property ideals. What most people mistake for private property is this fake kind where ownership determines law. Like the corporations who copyright songs, and seek to police anyone who sings the songs. Thats not real libertarianism, that is just anarcho-capitalism, where unconstitutional owners become a government like entity with the ability to run like a dictatorship.
Libertarianism is designed to keep government out of the daily lives of citizens. When Libertarian Party candidates run for office, this is often the stance of the person. In general, the party wants to expand gun ownership, reduce government funding, recall the armed forces to within our borders and strengthen international relations through diplomatic means.
Libertarianism principles include, but are not limited to, individual rights, the rule of law, and limited government. The current members that make up the Libertarian party, like any political party, may be more left or right leaning. However, in general, the Libertarian party may be enjoying a slight upsurge the past few years because of the adherence to the belief in these 3 core principles.