Toe up socks are becoming more and more common in the western world--(where cuff down has predominated for centuries) and are most likely the original style for knitting socks.
Toe up socks are most often started with an invisible cast on. There are many style of casting on and starting a toe up sock—some start with as few as 3 stitches, or as many as 20.
Some of the more common styles of cast on include;
This list is not definitive, but just the more commonly used options. There are other cast ons choices, including some that are seamed, but most knitter (and wearers!) prefer un-seamed toes.--See Page 1 of the Cast On Tutorial for video links to instructions to most of these cast ons.
Vary as much as anything else. Some sock have pointed toes (that are start with very few stitches), others have trapezoidal toe shapes (one of the most common choices), round (dome) shapes, several with swirls, and a tapered shape known as star.
Novelty shapes include asymmetrical/more anatomically correct shaping. (right and left leaning toe tips) Because knitting has the ability to stretch in all directions, almost all of these different styles are comfortable--on most!
Most often, the toe is knit in plain stocking knit, but in the case of stranded color work socks, the pattern is often starts at the very first row. Conversely, some otherwise plain socks have toes knit with two strand of yarn, for durability. There simple are no hard and fast rules for sock knititng.
Most often the sole of the foot is worked in stocking knit—though some prefer reverse stocking knit on the sole –especially when the sock are knit with thicker yarns, at a coarser gauge (i.e., boot liner socks knit with worsted or aran weight yarn.)Soles with reverse stocking knit are sometimes called "princess soles".
In stranded color work socks, there are (frequently) more elaborate patterns on the instep, and simpler patterns on the sole.
Pattern work that involves cable, lace or other complex stitch patterns is usually omitted on the sole (which is worked in stocking knit or reverse stocking knit),with the patterning only worked on instep till after the heel.
There are many ways to form/shape the heel. The oldest style is the the Turkish heel, which was knit last, and involved binding off, then casting on, (leaving an opening on the underside of the sock) after the leg was finished, stitches were picked up from the bound off edge, and the cast on edge, and the heel was worked in the round, with shaping similar to the toe. Today, knitters rarely bind off and cast on stitches but use waste yarn or stitch holders, creating a similar(but smoother) effect.
Flap, turned and gussets heels can be worked on toe up socks–either with the flap on the sole of foot, in a standard F/T/G style—just worked in reverse.
The other option is a 'reverse engineered' F/T/G style heel. This is done with the gussets being worked first (by increasing, not decreasing) then the turning--worked on the center of sole, and finally, the flap being worked, flat, in short rows, with decreases worked, at the same time, to take up the extra stitches. This second option, while created by a total different technique, looks virtually the same as a cuff or top down style F/T/G heel.
Mitered short row heels are probably the most common option for toe up socks—the fit of this style heel can be improved with small gussets at the side to provide needed ease at this largest part of the foot. There are various methods for creating gussets.
Mitered short row heels come in very many variations, some with specific names, (like the Fish Lips Kiss variation) Other varitions may or many not have specific names.
A common variation is to work gussets (there are several styles of gusset use with short row heels) The gussets make the short row heels deeper (and fit better for those with high insteps)
The newest heel (for toe up or cuff down heels) is Lucy Neatby's Sweet Tomato Heel. It's work with short rows to create a small wedge, and 2 or 3 wedges are stacked one after another to create the heel.
Afterthought heel or a pre-planned “afore thought” heel— are similar in appearence. The afterthought heel starts on the sole/back of a simple tube sock. A single stitch is snipped with a scissor, and a half row of stitching is undone. The life stitches are picked up as they become available. Once all the stitches are picked up, the heel is knit with a new ball of yarn. The tails from undoing the row of knitting are woven in.
The aforethought heel is very similar, but its position is preplanned, and a half row of waste yarn is used to create life stitches for pick up.
After the body of the sock is complete, the waste yarn is cut and removed, the live stitches picked up, and the heel completed.
There are several types of heels that can be created--the heel can be shaped like a toe, with paired decreases or they can be shaped like a hat, with sets of decreases that swirl. After thought heels can be matched--when using self striping yarn, (on the back of heel) to continue the stripe pattern of self patterning yarns.. (a nice detail if you wear open back shoes or clogs.)
There is also a style of heel called the gusset heel--which is worked with Increases and decrease, and no short rows at all
Less common styles include the Cuban heel, and novelty heels.
The leg of the sock can be plain, a continuation of the instep pattern, or new pattern. It can be short (anklets) or long (knee highs, or over the knee ) it can be shapeless or shaped—taller socks (knee high) socks often require shaping (by increasing)to fit. The shaping can be done on the sides, or center back or worked into the pattern. There is almost an unlimited choice of stitch patterns for the leg of the sock.
Some socks legs are knit flat (not in round) and incorporate intarsia or other patterns that are not well suited to working in the round.
Cuffs in socks serve the function of helping to hold a sock up. The most common cuff treatment is ribbing of some sort, but welting (single, double or other forms of garter stitch) can work just as well, as can other decorative trims. Cuffs can be narrow (10mm/1 inch or under , or deep (15mm/3 inches) or more, and folded back to double thickness. Cuffs can also be knit crosswise to the main body of the sock.
The most important consideration for the bind off, is stretchines—a too tight bind off can ruin the comfort of an otherwise perfect pair of socks, making them hard to put on or take off, and binding at the top when worn.
Some excellent choices include:
See the Cast on and Bind off tutorial for video links to these and other suitable bind offs.