They range from tassels to cords, lace, velvet and ribbons.
The most important thing to remember is to keep the scale, weight and proportion in keeping with the dimensions of the curtain.
To follow are a few types that are available, most come in natural fibers and synthetic fibers, the luxury end of trims are often made from silk or linen. Often rayon or viscose is added to cotton or wool to provide sheen to them.
Braid
Is a woven ornamental trimming that has two finished edges, it is a flat border. It was popular for placing over finished edges of upholstery on chairs.
Gimp
This has looped or scalloped edges and is a narrow type of braid. It is often used to cover over upholstery tacks on chairs.
Loads of trim used on the curtains in this period ballroom.
Piping
Piping Is a product that can be stitched into the seam of a curtain. It is a fabric-covered cord in a pipe like fold over cord with a narrow flange. It provides a subtle detail to drapery and is a good way of introducing a highlight color. It is used extensively with cushions and not as popular with curtains because it is labor intensive to make.
Buttons can be covered in fabric or selected off the shelf, they are used to pull two pieces of fabric together for example a cushion pulled in the center, or create a design - the back of a chair can be buttoned creating a padded look i.e. Chesterfield.
With curtains they can be used with French Pleats to hold the pleat together at the base and create a stunning look if used in a contrasting color. They are often used on tiebacks, and are a decorative feature on valances when used to hold tassels.