Paper as a material is cheap, lightweight, bendable, fold-able, sleek, aerodynamic, absorbent, cut-able, punch-able, stack-able, mark-able, roll-able, printable, flammable and see-through.
It is relatively sturdy and highly compressed but also flimsy and rip-able or shear-able.
It can even be used as an instrument depending on the stiffness of the paper when waved or flicked or patted like a drum; rolled up and used as a bat.
It is also a building material, paper screens providing privacy or some newspaper on a window, or on a windowless building, paper pasted around framed openings can provide some protection from the wind and cold.
If you crumple paper up, it becomes a ball, or if folded tightly into a triangle, a paper football. Also, there are paper airplanes.
Of course, paper makes up books, magazines, receipts, currency, packaging, wrapping. However, these are made up of other materials.
There are many paper products that are similar in quality.
It is ubiquitous in crafting processes as a tool for measuring, prototyping, and as a waste byproduct in absorbing liquids and in forging metals that must be held together briefly.
Paper is fibrous. In paper chromatography, the paper is used to separate substances by distance traveled through capillary action. What causes pigments as in water color, ink, or graphite to stick to a page? Are these particles becoming trapped within the fibers of the paper?
Paper is treated chemically for magic or scientific purposes as in an invisible ink demonstration or flash paper, or as pH paper or a different test kit. Paper can also form a funnel or shoot or be used as a filter. Paper can also be used to view a solar eclipse through a pinhole.
Paper is also quite sharp with a cutting edge. It can be slid under or through objects like skin. It can be used to hide or press objects as in pressing plants or hiding objects in a book.
China and Japan are well known for their paper-crafts. From Japan, there is origami or paper folding. From China, there is Jian3zhi3 剪纸 or paper cutting art. A thin often red paper is cut very precisely creating a negative pattern of an object. These flat pieces of art are reminiscent of Chinese shadow puppetry, Pi2Ying3Xi4, 皮影戲. Also, there is kite and lantern making.
In origami, folders manipulate the paper into convex and concave areas that form creases in new areas. Another form of origami called kusadama fits together repeating elements to create geometric shapes. In some forms of origami, cutting and gluing are permitted.
In the west, generally, paper craft took a different form. There is papier-mâché which is used to make models, puppets, dolls, or a piñata. There are paper boats and hats that can be made out of newspaper. The boats are waterproofed with a sealant. Streamers used as decoration. Confetti thrown at parties. Another party favor is the cascarón which is an egg filled with confetti that is sometimes attached to a paper cone and used to hit people over the head.
Other paper crafts include bookbinding, collage, scrap-booking, and printing or mimeographing office or promotional materials, posters, menus in mass production.
An interesting aspect of some paper products is the perforated edge. How is a perforated edge made? Is there any waste when you make a perforated edge like in hole punching? A paper can be creased a few times and carefully pulled apart but the edge will look rough. Separating a perforated edge, the sound it makes, is one of the small pleasures in life. (I wonder also if you can achieve an optical effect by shining light through a perforated edge.)
Another use of thin paper is in relief drawings where by taking charcoal or graphite you can take a rubbing of a textured object.
Thicker paper and other sturdier material like cardboard allows the creation of more rigid structures like models.
In cardboard, corrugation, placing a wavy piece between two flat pieces, creates cells in the shape of trapezoids. Thus is it also pin-able.
Cardboard or any thicker piece of paper, card stock, can be built up in layers to create a 3D model like a topographical map. Architectural models often employ this technique to create a landscape or foundation on which to place a structure which can also be made of construction paper. A model of a building is created by adding elements together rather than subtracting pieces from a single material as in sculpture. The creation of models by layers is like sculpture and the technique is the same one used in calculus to approximate volume by slices.