This article examines monetary policy when it is constrained by the zero lower bound (ZLB) on the nominal interest rate. Our analysis uses a nonlinear New Keynesian model with technology and discount factor shocks. Specifically, we investigate why technology shocks may have unconventional effects at the ZLB, what factors affect the likelihood of hitting the ZLB, and the implications of alternative monetary policy rules. We initially focus on a New Keynesian model without capital (Model 1) and then study that model with capital (Model 2). The advantage of including capital is that it introduces another mechanism for intertemporal substitution that strengthens the expectational effects of the ZLB. Four main findings emerge: (1) In Model 1, the choice of output target in the Taylor rule may reverse the effects of technology shocks when the ZLB binds; (2) When the central bank targets steady-state output in Model 2, a positive technology shock at the ZLB leads to more pronounced unconventional dynamics than in Model 1; (3) The presence of capital changes the qualitative effects of demand shocks and alters the impact of a monetary policy rule that emphasizes output stability; and (4) In Model 1, the constrained linear solution is a decent approximation of the nonlinear solution, but meaningful differences exist between the solutions in Model 2.