This section evaluates different ways of making textiles given a somewhat abritrary criteria.

weaving a process in which two types of thread or yarn are interlaced together the two types of threads run in different directions, with the warp threads running length-wise as the weft threads get inserted horizontally. In weaving threads are always straight and perpendicular to each other. The most common means of producing woven textiles is on a machine called the loom, which can be configured to produce both flat sheets as well as circular structures of fabric.
open source options: OSloom : an open source Jaquard loom that never posted it's models, files, etc. Pamela Liou's loom is also undocumented.
clothing / final product: because woven fabrics are typically made in sheets or tubes, they are less suitable for "printing" a garment and would require tailoring. Read more on how clothing is made here.
etcetera: there have been a number of studies comparing different kinds of woven fabrics as well as their mechanical properties here are two papers on the subject matter:
Development of the Weaving Machine and 3D Woven Spacer Fabric Structures for Lightweight Composites Materials thesis by Said Sobhey Badawi
3D Woven Fabrics

knitting unlike weaving knitting typically uses a single source of yarn that loops onto itself, over and under the established path. This gives knitted fabrics greater flexibility. It also allows for a greater contour control.
open source options: Open-Knit is a great project with both a github repository and instructables tutorial available. Open-Knit's github repository even features a 3D model of it's machines – e.g. here's a model of Wally 120. The initiative "spun" itself off into a start-up called Kniterate, priced at ~$6,500.
Circular Knitic is another well-documented project with both a github repository and instructables tutorial available. Mar Canet, a collaborator on the Knitic project has also written processing sketches for the Brother KH930 and KH940 electronic knitting machines to replace the machines' existing electronics with an arduino.
clothing / final product: since knit fabrics are typically stretchy there is less tailoring that needs to take place and thus making a garment from a knit requieres less seams – think of a dress shirt relative to a T-shirt for example.
The Singer 560 electronic knitting machine manual (pages 56-70) gives a resonable explanation of how to create a range of knitwear.
Here's a cool research project (thanks Jake!) on converting 3D meshes into instructions for a computer-controlled knitting machine.
etcetera: a paper with a comparison of mechanical properties of woven and knit fabric for composites.
Interestingly, knitting offers a multiaxial option as well called inlay knitting – a method that introduces stuffer threads into the knit. Here's a course with more information on the subject matter.
For aesthetic purposes it is possible to create elaborate patterns with knitting by varying the colors of threads a common technique called short row knitting is tyically used to achieve this.

crochet chrochet is a method, similar to knitting, that manipulates loops of yarn with typically one active loop the chrochet doesn't lend itself to unraveling during the production process. There do not seem to be active DIY chrochet projects, it's a method that remains confined to a craft domain with very little automation. Mainly because unlike knitting the process entails multiple loops on one needle rather than multiple stitches on multiple needles as seen in the knitting machines.

felting is produced by matting, condensing and pressing fibers together – there is no stitching or looping involved. Needle felting does not require water to form fibers into place – this is the type of felting that has seen greatest automation. Currently the Textile Academy is working on a felting machine.

braiding / plaiting is produced by interlacing three or more strands of flexible material.
open source options: Stig Anton Nielsen's open source modular machine.