5.1. Smooth  S

Gently smooth out a curve.

5.2. Smooth More  Ctrl+S

Strong smooth effect on a curve.

5.3. Add Curve from Clipboard

Select a curve and Copy it to the clipboard. Then you can reuse the curve in other Curvy Objects with Add Curve from Clipboard.

5.4. Replace Curve with Clipboard

You can't create a new object from a Clipboard Curve, so you need to draw any curve to create the object then select that curve and Replace it with the curve on the clipboard.

5.5. Clone

Make a clone of this curve in place. You will need to move the new curve away from the original to see them separately.

5.6. Mirror Clone

Duplicates and mirrors the new curve.

Whereas "M" symmetry creates a virtual fourth line for a lathe object, Mirror Clone can be used to create a real fourth line opposite the third, and since this avoids using symmetry the map can be different on either side of the model.

5.7. Drop to Surface

Line up the Perspective view so your selected Curve lies over some other meshes. Drop to Surface will move the selected curve onto the other objects in the direction of the Perspective View.

5.8. Align Curve to Axis

This rotates the curve a little bit to make the endpoints line up with the axis directions. This is useful for straightening a freehand drawn shape.

5.9. Curve Reverse

Swaps the start and end points of a Curve.
Sometimes useful to correct the direction of Curves in a Lathe or Loft to match the object's other curves.

5.10. Extract Mesh Boundary

On a mesh with a hole, or a masked area of a mesh this creates new Sketch Curves than run along the edge of the holes/mask.

These can then be copied and reused to make other Curvy Primitives such as Lines and Proxy Rails.

5.11. LoadBezier

Create an object with curves (can just be a Sketch Object) then use LoadBezier to fill it with the curves from a SVG file.
If you bring in several curves you can separate them out with Copy and "Add Curve from Clipboard", or by duplicating the object and deleting the unwanted curves.
You can import text, or intricate patterns from SVG files made in software like Inkscape.

5.12. Redraw As...

Redraws an entire curve to fit a precise shape.
To make accurate geometric curves and perfect spheres and ellipses use these commands to turn rough shapes into exact curves. Redraw As... Semi-Circle is especially useful for making spheres, Redraw As... Straight-Line helps make flat planes out of loft objects.

5.13. Curve Mirror

Make a Curve symmetrical from Left to Right, or Top to Bottom compared to the grid.

5.14. Lathe Auto Curve

Adds extra curves to a Lathe object to turn it into a 2,3 or 4 line Lathe ready for further editing.
This saves having to manually copy, mirror or rotate the extra curves into place yourself.

Adds a mirrored Curve opposite the original curve.
Adds a back and side curve, and automatically sets up Lathe Symmetry so the side is mirrored to the other side.
Adds curves to make a 4 line lathe with front, back, left and right curves.

5.15. Optimise

Reduces the point count in the current curve.

5.16. Draw Smooth Lines

By default curvy applies heavy smoothing to each drawn curve.

5.17. Draw Precise Lines

Choose this option to allow raw unsmoothed curve drawing.

5.18. Draw Bezier Path

This option will create a Bezier Path controlled by handles instead of a freehand curve when you draw.
The first line creates an initial node in the path - then you can use the Bezier Curve Tools to create and edit the rest.