Growing up on the cryptic crosswords I found in Games magazine and The New York Times, I'm used to a very rigid rule for clues: Every clue comprises two parts, one of which directly (if opaquely) clues the word as in a non-cryptic crossword and the other of which does so cryptically. (These may be separated by "is" or "to yield" or some similar copula. And so-called &lit clues are an exception.) The cryptic half, in turn, has some fairly rigid rules: If it uses an anagram, it must indicate as much (thus, e.g., "turned handle" for HANDEL, never just "handle" for HANDEL); and if it hides a word within another, it must indicate as much (thus, e.g., "in the best" for THEBES, never just "the best" for THEBES).
But I've seen cryptics — mostly, I think, from Britain — whose clues don't follow these rules. They seem to allow anagrams and words hidden within other words even without signaling as much, and they even seem to allow cryptic-half-only clues, without a non-cryptic component of the clue. What rules, if any, do such crosswords follow for clue composition?