This thesis explores the hierarchy problem of the Standard Model of particle physics, its natural solutions, and the collider and cosmological signals of such theories. A review of the hierarchy problem is presented along with some of the model building tools used to solve it, followed by a complementary review of extra dimensional models which emphasizes their relation to the hierarchy problem. Several new ideas for addressing the hierarchy problem are presented in this thesis as well as their experimental manifestation. Aspects of models which exhibit neutral naturalness are explored, and it is shown that Twin Higgs models with a full mirror sector can be cosmologically viable. New signals of such a scenario include an excess contribution to the dark radiation energy density measured by the the cosmic microwave background and sterile neutrino signals at future beam dump experiments. The method of searching for long-lived Higgs boson decay products at the Large Hadron Collider is presented as the best strategy for constraining models of neutral naturalness. Another category of natural models with long-lived particles, supersymmetric models with R-parity violation, is explored and the leading bounds are derived. Finally, several ideas which were introduced to explain the infamous 750 GeV excess of 2015 are provided.