This paper describes a microfluidic approach to generate dynamic temporal and spatial concentration gradients using a single microfluidic device. Compared to a previously described method that produced a single fixed gradient shape for each device, this approach combines a simple "mixer module" with gradient generating network to control and manipulate a number of different gradient shapes. The gradient profile is determined by the configuration of fluidic inputs as well as the design of microchannel network. By controlling the relative flow rates of the fluidic inputs using separate syringe pumps, the resulting composition of the inlets that feed the gradient generator can be dynamically controlled to generate temporal and spatial gradients. To demonstrate the concept and illustrate this approach, examples of devices that generate (1) temporal gradients of homogeneous concentrations, (2) linear gradients with dynamically controlled slope, baseline, and direction, and (3) nonlinear gradients with controlled nonlinearity are shown and their limitations are described.