Most historians agree that early examples of the technique used in collage can be traced as far back as 200 BCE in China, when paper was first invented by Cai Lun. The technique was later popular in 10th century Japan where it was used by calligraphers and poets as they pasted words on various surfaces. In 10th to 11th century this technique was developed in Japan and called Chigiri-e (ちぎり絵) which it involved tearing pieces of dyed paper and combining them to create a scene. Still not widespread, the technique was again used in 15th and 16th century europe as a means of beautifying gothic cathedrals by attaching metals and gems to religious artworks. 

Chigri-e example: Purple Mountains Majesty by Barbara Harmer

In the 19th century this technique was seen more frequently as scrapbooking became popular. Finally, in the early 20th century the term "collage" was coined to refer to cubist works by Pablo Picasso and Georges Braque that were cut snd pasted together in their assemblages. These techniques were immediately incorporated into the the following art movements of Dada and Surrealism and became crucial parts of the storytelling surrounding World War I. Later, collage had a large influence on the Pop Art movement. 

Through combining a variety of elements, artists who created collages within the Dada movement were celebrated for their creative use of presumably worthless and frequently disregarded objects. These items often included magazine cut-outs, candy wrappers, tickets, and various three-dimensional ornaments. Through transforming transient ideas and materials into more refined pieces, Dadaists were able to call into question traditional perceptions of art. - artincontext.org

Considered a form of mixed media, of which there are many types, there are also quite a few types of collage. 

Photomontage is one type in which the artist uses only photographs in their work. 

Similarly, Papier Collé works are created using only decorated, dyed, and printed paper of all kinds to achieve their final design.

Decoupagé artists use flat materials to decorate an object of choice which is finished with a laquer or varnish sealant. 

Assemblage works are typically 3D and include any variety of materials, oftentimes found items are incorporated in these works.

Mosaics are typically created by using glass, tiles, or rocks in patterns to create an image. This is usually to make organic images such as scenery or portraits. 

Digital collage uses various software (like Adobe) to cut and paste any item that can be digitized and reconfigured.