This paper pursues a line of Cass and Shell, who advocate monetary models that are "genuinely dynamic and fundamentally disaggregative" and incorporate "diversity among households and variety among commodities." Recent search-theoretic models fit this description. We show that, like overlapping generations models, search models generate interesting dynamic equilibria, including cycles, chaos, and sunspot equilibria. This helps us understand how alternative models are related, and lends support to the notion that endogenous dynamics and uncertainty matter, perhaps especially in monetary economies. We also suggest such equilibria in search models may be more empirically relevant than in some other models.