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The ground to address challenges in demand load control for the smart power grid is now more fertile than ever, due to advances in communication infrastructures and the creation of a two-way channel for real-time communication between consumers and the utility operator. After giving a taxonomy of methods for demand load control, we focus on two of these methods that aim at minimizing the grid operational cost. The cost is a convex function of instantaneous power consumption and reflects the fact that each additional unit of power needed to serve demands is more expensive as the demand load increases. First, we consider online scheduling of power demand tasks that have time flexibility in being activated, in terms of a deadline. We outline the rationale for threshold-based policies that activate a demand if the instantaneous consumption is low; otherwise, they postpone it until later. Second, we discuss the use of stored energy for serving part of the demand at peak load times. This implies increasing the demand load at off-peak times through battery charging and decreasing the demand load at peak load times through discharging. We conclude with some open challenges in demand load management.