Th is a digraph in the Latin script. It was originally introduced into Latin to transliterate Greek loan words. In modern languages that use the Latin alphabet, it represents a number of different sounds. It is the most common digraph in order of frequency in the English language.
The most logical use of ⟨th⟩ is to represent a consonant cluster of the phonemes /t/ and /h/, as in English knighthood. This is not a digraph, since a digraph is a pair of letters representing a single phoneme or a sequence of phonemes that does not correspond to the normal values of the separate characters.
⟨th⟩ is used in academic transcription systems to represent letters in south and east Asian alphabets that have the value /t?/. According to the Royal Thai General System of Transcription, for example, ⟨th⟩ represents a series of Thai letters with the value /t?/.
During late antiquity, the Greek phoneme represented by the letter ⟨?⟩ mutated from an aspirated stop /t?/ to a fricative /?/. This mutation affected the pronunciation of ⟨th⟩, which began to be used to represent the phoneme /?/ in some of the languages that had it.
The Old English Latin alphabet adapted the runic letter ⟨þ⟩ (thorn), as well as ⟨ð⟩ (eth; ðæt in Old English), a modified version of the Latin letter ⟨d⟩, to represent this sound, but the digraph ⟨th⟩ gradually superseded these letters in Middle English. However, in early Old English of the 7th and 8th centuries, the runic letters were initially not used yet and the digraph used in its place.
In modern English, an example of the ⟨th⟩ digraph pronounced as /?/ is the one in tooth.
English also uses ⟨th⟩ to represent the voiced dental fricative /ð/, as in father. This unusual extension of the digraph to represent a voiced sound is caused by the fact that, in Old English, the sounds /?/ and /ð/ stood in allophonic relationship to each other and so did not need to be rigorously distinguished in spelling. The letters ⟨þ⟩ and ⟨ð⟩ were used indiscriminately for both sounds, and when these were replaced by ⟨th⟩ in the 15th century, it was likewise used for both sounds. (For the same reason, ⟨s⟩ is used in English for both /s/ and /z/.)
Because neither /t?/ nor /?/ were native phonemes in Latin, the Greek sound represented by ⟨th⟩ came to be pronounced /t/. The spelling retained the digraph for etymological reasons. This practice was then borrowed into German, French, Dutch and other languages, where ⟨th⟩ still appears in originally Greek words, but is pronounced /t/. See German orthography. Interlingua also employs this pronunciation.
In early modern times, French, German and English all expanded this by analogy to words for which there is no etymological reason, but for the most part the modern spelling systems have eliminated this. Examples of unetymological ⟨th⟩ in English are the name of the River Thames from Middle English Temese and the name Anthony (though the ⟨th⟩ is often pronounced /?/ under the influence of the spelling) from Latin Antonius.
In Irish and Scottish Gaelic, ⟨th⟩ represents the lenition of /t/. In most cases word-initially, it is pronounced /h/. For example: Irish and Scottish Gaelic toil [t?l?] 'will' -> do thoil [d? h?l?] 'your will'.
This use of digraphs with ⟨h⟩ to indicate lenition is distinct from the other uses which derive from Latin. While it is true that the presence of digraphs with ⟨h⟩ in Latin inspired the Goidelic usage, their allocation to phonemes is based entirely on the internal logic of the Goidelic languages. Lenition in Gaelic lettering was traditionally denoted in handwriting using an overdot but typesetters lacked these pre-composed types and substituted a trailing h. It is also a consequence of their history: the digraph initially, in Old and Middle Irish, designated the phoneme /?/, but later sound changes complicated and obscured the grapheme-sound correspondence, so that ⟨th⟩ is even found in some words like Scottish Gaelic piuthar "sister" that never had a /?/ to begin with. This is an example of "inverted (historical) spelling": the model of words where the original interdental fricative had disappeared between vowels caused ⟨th⟩ to be reinterpreted as a marker of hiatus.
The Irish and Scottish Gaelic lenited /t/ is silent in final position, as in Scottish Gaelic sgith /ski:/ "tired". And, rarely, it is silent in initial position, as in Scottish Gaelic thu /u:/ "you".
In English the ⟨th⟩ in "asthma" and "clothes" is often silent.
ᵺ LATIN SMALL LETTER TH WITH STRIKETHROUGH is used for phonetic notation in some dictionaries.