The importance of relating micro-level interactions with macro-level phenomena in modeling social dynamics is now established, and the study of parsimonious models has received growing interest in the last two decades. I will discuss some aspects of the celebrated voter model on which Sid Redner has done seminal work. Sociological studies indicate that heterogeneous responses to stimuli, the seek for consensus, and some form of limited compatibility may be important ingredients for modeling social dynamics. In this context, I will discuss the influence of the presence of zealots on the long-time dynamics of the two-state and three-party constrained voter models. In the former case, we shall determine the circumstances under which a single zealot imposes its opinion to an entire population, and will discuss the influence of competing zealots. We will also see that polarization can arise in the three-party constrained voter model, where individuals of two radical parties are incompatible between them but interact with “centrists.” In this case, the presence of some committed centrists (zealots) suffices to resist and eventually overcome the persuasive power of radical agents.