Performance origami is about using paperfolding to produce entertaining, amusing, or sometimes magical, effects. There are two different kinds of performance origami:

Performance origami in which the effect lies in the folding process itself, usually in a 'surprise' denouement to the folding sequence.

Performance origami in which the effect is achieved by the manipulation of the finished paperfold. Troublewit is a classic example.

Craft origami is what most people would think of when they hear the word origami. Craft origami embraces both the process of creating designs that are intended to be reproducible and the process of reproducing them from personal or recorded tuition, from diagrams, or by reverse-engineering.

The reproduction part of craft origami is not a sterile process. In reproducing the chosen design the folder seeks to personalise it - by careful choice or manufacture of the paper, by the application of folding and finishing skills, and often also by varying the finishing folds to produce an enhanced aesthetic effect.

Craft origami can be divided into representational, abstract, play and functional origami. There are individual notes on each of these

This is not as crazy as it sounds. Experienced model-making paperfolders can often look at a paperfold for the first time and reconstruct the basic folding sequence in their minds. It is a short step from that to being able to visualise a finished model that you want to design and 'unfolding' it to work out how it could be made.

In addition, origami designers, particularly result-orientated designers working in the model-making field are increasingly using mathematical design techniques and only realising their models in paper once the design process is at an advanced stage.

Origami puzzles are puzzles which relate to the qualities and configurations of folded paper.

Origami puzzles come in two distinct kinds - those which can be solved by trial and error while folding or manipulating paper (a form of exploratory origami) and those which can only be solved by mathematics (perhaps a form of virtual origami).

It is important to distinguish between origami puzzles and origami models of puzzles which were originally designed in another medium such as plastic or wood. The folding of such models is a type of model-making origami.

This can be done either by the merest suggestion (minimalist origami) or by attempting to achieve a high degree of verisimilitude (model-making origami).

Play origami is a form of craft origami concerned with the realisation of paperfolds which can function as manipulative novelties or toys. Many traditional paperfolds - including the Flapping Bird - fall into this category.

Playground folds are folds which are in common use by children in the playground. In UK the most common playground folds are the basic paper dart from a rectangle and the Fortune Teller from a square. (Playground folds could also be considered to be a form of Everyday Origami.)

Paper Aircraft are a variety of play origami, but one that is now taken quite seriously in some quarters (thanks largely to the Guinness Book of Records).

Flexagons are fascinating novelties made by folding and weaving strips of paper into polygonal forms. These forms can be flexed in many intriguing ways to alter the appearance of their visible surfaces. Flexagons are not strictly origami - but are definitely origamic.

Origami Games are games specifically designed to be played by folding paper or which require paperfolds as essential apparatus (eg Jumping Frog races). Making folded paper versions of existing games that normally using apparatus made of other materials (eg origami versions of Tangrams) is a form of model-making origami.

Usually such forms are produced by straight-line folds alone, but the use of curved crease lines is becoming more common. Straight-line folds in one part of the paper can also be used to induce curves in other areas of the same sheet..

Abstract origami forms are generally either single-piece or modular. Modular origami is a technique in which sheets of paper are folded into modules or units which are then combined into two or three-dimensional abstract forms.

Functional origami is a form of craft origami that is intended to serve a practical purpose around the home or in the work-place.

Most functional objects - containers, photo-frames, stands etc - are single-piece paperfolds, though there are many excellent modular boxes.

Ornaments may be considered a form of functional origami. Most of the best origami ornaments are modular, though there are some fine single-piece designs as well.

Minimalist origami is a form of representational origami that seeks to capture the essence of a subject in the smallest possible number of folds (usually between 1 and 5 - though there is no hard and fast rule).

Many minimalist folds are pictorial, since this technique dramatically increases the representational potential of a few simple folds.

Model-making origami seeks to model plants, living creatures, or inanimate objects in folded paper.

Enthusiasts for this type of origami often subscribe to the ethic that origami should be single-sheet and tend to prefer designs that are as realistic as possible.

This combination of the single-piece ethic and a desire for realism brings the designer straight up against the limitations of paperfolding technique, so it is not surprising that most of the advances in single-sheet origami technique have been achieved by designers working in this field.

Model-making origami is the most popular form of craft origami. Indeed many paperfolders (even paperfolding clubs) tend to concentrate on this form of origami to the virtual exclusion of everything else.

Geometric origami is often produced as a by-product of exploratory origami. It is important to realise that although its value in terms of exploratory origami may be high this does not necessarily translate into value as craft origami. Unfortunately too many badly differentiated examples of this type of origami are diagrammed (often on a stream-of-consciousness basis) with the result that the (much rarer) good quality work produced in this style is often under-valued.

Many designers have produced single-sheet sculpture using techniques which vary from twist folding through cross-pleating to random crumpling.

Modular sculpture is abstract sculpture produced by modular origami.

Macro-modular sculpture is abstract sculpture produced by combining simple modular assemblies into larger structures.

Mathematical modelling means the folding of polyhedra or tiles/tiling patterns.

Tiles and/or tiling patterns are usually folded from multiple single-sheets.

Polyhedra can be folded either from single sheets or, usually more effectively, from modules.

In a similar vein, modular origami has been used to model molecular structures, particularly the structure of fullerenes.