Because control points define the contours of a complex shape, you can move control points to change the shape.
For all of the following procedures, use the Edit Points tool in the 2D transform tools pop-up menu.

Tip: You can also modify multiple control points across different shapes simultaneously by selecting them all at once.
Select control points on the shape in the Canvas, then drag the points to a new position.
As you drag selected control points, the rest of the shape stretches or curves to accommodate the change.

Press Command–Left Arrow, Command–Right Arrow, Command–Up Arrow, or Command–Down Arrow to nudge a point by one pixel (or Shift-Command to nudge by 10 pixels).
Select control points.
Press Shift while you drag a selected point horizontally, vertically, or diagonally.
Important: To rotate or scale control points, you must use the Transform Control Points command. See “Transform a group of control points,” below.
You can scale and rotate a group of points as if they were a single object by using the Transform Control Points command. The lines connecting the selected points to unselected points will move and adjust.
Drag a selection rectangle around the points you want to modify.
Choose Edit > Transform Control Points or press Shift-Command-T.
A bounding box appears around the selected points.
Note: The Transform Control Points command is available only when at least two points on the same spline are selected.
Drag bounding box handles to scale, rotate, offset the anchor point, and reposition the group of points as if they were a single object.
To release the selection, click anywhere outside the selection, or switch to a different tool.
You can also select the line between two control points and drag the edge of the shape.
Click any edge of a shape object.
The control points on either side of the line are selected.
Drag the line segment.

The distance between the two points remains constant, but the line can be moved freely. Press Shift to constrain the movement horizontally, vertically, or diagonally.
To release the selection, click anywhere outside the selection, or choose a different tool in the toolbar.