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Why do people change their minds and what are the consequences? This talk will discuss several models that use approaches from statistical physics and nonlinear dynamics to analyze opinion dynamics in social systems. First are voter models that relate to contact processes on networks and reveal the defining role that zealots play in driving social outcomes. Second is how we can use the Fokker-Plank equation to show that homophily between individuals, which is meant to increase social cohesion, can actually impede global consensus. Finally we will use results from bifurcation theory to show how the competition between rewarding talent and rewarding social reputation can cause cascading rank rearrangements in established social hierarchies. The main work highlighted appeared in Phys. Rev. Lett. 125, 078302 (2020) and Phys. Rev. E 98 (2), 020302 (2018).