First up is one of the oldest modes, but it is still used widely. It's usually called RTTY, for Radioteletype. In the military, you'll also see references to RATT, also Radioteletype.
RTTY's earliest precursor is the Baudot telegraphy code developed in the 1870s by two people working for Jean-Maurice-Émile Baudot, a French engineer. (Yes, that's where we get the transmission speed unit "baud.") This was a 5-bit code, that became known as International Telegraph Alphabet #1 (ITA1, no longer used).
The Baudot code was improved by Donald Murray and others in the early 20th century, leading to an originally Western Union wireline standard called ITA2. This is still the one used for basic English-language Baudot teleprinting. It is still a 5-bit, 32-state, 58-character code, with longer pauses marking start and stop of characters. The name "Baudot" for ITA2 is not technically correct, but in practice the two names are interchangeable. Several ITA alphabets with higher numbers exist for use in other languages, and of course we don't even have time to talk about "third shift" modes for such non-Latin character set languages as Russian.
ITA2 has no lower case. The cases are LTRS (Letters; all upper case) and FIGS (Figures; numbers and punctuation). The case is changed by transmission of control characters corresponding to each. Since the normal mode is letters case, they can also be regarded as shift in (to figures) and shift out. A missed shift character leads to gibberish, and most RTTY systems have the option USOS (Unshift On Space) as a partial (and only partial) solution.
ITA2 bit states are based on timing, and they do not correspond to the base-2 places used in binary numerical notation, which was not used in mechanical teleprinting. Since a bit is technically a "binary digit," we should probably be calling them something else, but we won't. However, note how many of the ITA2 control characters carried over, with bit changes, into later binary computer codes such as American Standard Code for Information Interchange (ASCII).
The 5 bits were typically stored by punching holes in paper tape run through a perforator machine from reels resembling 16-mm movie film. These were read by tape keyers, which controlled a "current loop" connected to a "terminal unit" that interfaced with mechanical teleprinting machines. Many of these were made by the Teletype Corporation, and so "Teletype" is actually an old business trade name, though it has become somewhat generic.
Messages could be relayed by "reperforating" at the receive site. Note that the character pair RY is sent with alternating 01010 and 10101, testing all possible bit states in the code. Even in this electronic age, the test "slip" RYRYRY..., sometimes accompanied by THE QUICK BROWN FOX... is still common.
Here is the ITA2 code (click for bigger image):
