Uncial is a majuscule script (written entirely in capital letters) commonly used from the 4th to 8th centuries AD by Latin and Greek scribes. Uncial letters were used to write Greek, Latin, and Gothic.
Early uncial script most likely developed from late rustic capitals. Early forms are characterized by broad single-stroke letters using simple round forms taking advantage of the new parchment and vellum surfaces, as opposed to the angular, multiple-stroke letters, which are more suited for rougher surfaces, such as papyrus. In the oldest examples of uncial, such as the fragment of De bellis macedonicis in the British Library, of the late 1st-early 2nd century, all of the letters are disconnected from one another, and word separation is typically not used. Word separation, however, is characteristic of later uncial usage.
As the script evolved over the centuries, the characters became more complex. Specifically, around AD 600, flourishes and exaggerations of the basic strokes began to appear in more manuscripts. Ascenders and descenders were the first major alterations, followed by twists of the tool in the basic stroke and overlapping. By the time the more compact minuscule scripts arose circa AD 800, some of the evolved uncial styles formed the basis for these simplified, smaller scripts. Uncial was still used, particularly for copies of the Bible, tapering off until around the 10th century. There are over 500 surviving copies of uncial script, by far the largest number prior to the Carolingian Renaissance.
In general, there are some common features of uncial script:
In later uncial scripts, the letters are sometimes drawn haphazardly; for example, ⟨ll⟩ runs together at the baseline, bows (for example in ⟨b⟩, ⟨p⟩, ⟨r⟩) do not entirely curve in to touch their stems, and the script is generally not written as cleanly as previously.
There is some doubt about the original meaning of the word. Uncial itself probably comes from St. Jerome's preface to the Book of Job, where it is found in the form uncialibus, but it is possible that this is a misreading of inicialibus (though this makes little sense in the context), and Jerome may have been referring to the larger initial letters found at the beginning of paragraphs.
In classical Latin uncialis could mean both "inch-high" and "weighing an ounce", and it is possible that Jerome was punning on this; he may conceivably also have been playing with the other meaning of codex, "block of wood".
The term uncial in the sense of describing this script was first used by Jean Mabillon in the early 18th century. Thereafter his definition was refined by Scipione Maffei, who used it to refer to this script as distinct from Roman square capitals.
The word, uncial, is also sometimes used to refer to manuscripts that have been scribed in uncial, especially when differentiating from those penned with minuscule. Some of the most noteworthy Greek uncials are:
The Petropolitanus is considered by some to contain optimum uncial style. It is also an example of how large the characters were getting.
For further details on these manuscripts, see Guglielmo Cavallo Ricerche sulla Maiuscola Biblica (Florence, 1967).
Modern calligraphy usually teaches a form of evolved Latin-based uncial hand that would probably be best compared to the later 7th to 10th century examples, though admittedly, the variations in Latin uncial are much wider and less rigid than Greek. Modern uncial has borrowed heavily from some of the conventions found in more cursive scripts, using flourishes, variable width strokes, and on occasion, even center axis tilt.
In a way comparable to the continued widespread use of the blackletter typefaces for written German until well into the 20th century, Gaelic letterforms, which are similar to uncial letterforms, were conventionally used for typography in Irish until the 1950s. The script is still widely used in this way for titles of documents, inscriptions on monuments, and other 'official' uses. Strictly speaking, the Gaelic script is insular, not uncial. Uncial Greek (commonly called "Byzantine lettering" by Greeks themselves) is commonly used by the Greek Orthodox Church and various institutions and individuals in Greece to this day. The Modern Greek State has also used uncial script on several occasions in official capacity (such as on seals, government documents, etc.) as did many of the Greek provisional governments during the Greek War of Independence. The height of uncial usage by the Modern Greek State was during the Greek military junta of 1967-74, when even Greek Drachma coins had uncial lettering on them. Since the Metapolitefsi, the Greek State has stopped using uncial script.
The term half-uncial or semi-uncial was first deployed by Scipione Maffei, Istoria diplomatica (Mantua, 1727); he used it to distinguish what seemed like a cut-down version of uncial in the famous Codex Basilicanus of Hilary, which contains sections in each of the two types of script. The terminology was continued in the mid-18th century by René Prosper Tassin and Charles François Toustain.
Despite the common and well-fixed usage, half-uncial is a poor name to the extent that it suggests some organic debt to regular uncial, though both types share features inherited from their ancient source, capitalis rustica. 
It was first used around the 3rd century (if we don't consider its earliest example a transitional variant of the rustic script, as Leonard Boyle did) and remained in use until the end of the 8th century. The early forms of half-uncial were used for pagan authors and Roman legal writing, while in the 6th century the script came to be used in Africa and Europe (but not as often in insular centres) to transcribe Christian texts.
Some general forms of half-uncial letters are: