Using motion paths you can control how emitters, particles and force fields move over time. Motion paths are defined by waypoints, which you can add, remove and move as you like. To start editing a motion path of an object, select its Position property in the property panel.
To add a new waypoint, hold Shift and click on an empty spot in the scene view. Waypoints you add can be repositioned by moving them in the scene view. In order to remove existing waypoints, click on them while holding Shift. To change the timing of each waypoint and the path interpolation, use the keyframe editor.
In 2D, motion paths can be drawn as well. Click next to the Position property and then move the mouse over the scene view while holding the left mouse button. This automatically adds waypoints along the path you draw.