Cryptogram

A cryptogram, sometimes called cryptoquips or cryptoquotes depending on the encrypted content, are puzzles where a piece of text has been encrypted using an unknown-to-the-solver substitution cipher. To solve is, solvers need to pull knowledge of word structure, letter frequency, and possibly famous quotes or literary passages if the encrypted text is well-known.

Background
Cryptograms have been used for centuries as actual methods of encrypting messages and data, especially with regard to military operations. In terms of their use for entertainment, however, cryptograms originated in Europe in the middle ages. According to sources, monks would engage in games where ciphers were created and broken, including one that was purportedly given to a Welsh king in which the text had to be transposed from Latin to Greek as part of its solution.

One major spike in popularity of cryptograms coincided with some of Edgar Allan Poe's work, prompting him to center one of his short stories, The Gold-Bug, around a cryptogram. At the time, cryptography as a whole was considered to be an interesting and mysterious hobby, and Poe had published a challenge for any of his readers to send him cryptograms that they had made, claiming none would stump him. In the wake of this, and after publishing a piece titled "A Few Words on Secret Writing", he wrote The Gold-Bug to show how his methods could be used in a hypothetical scenario.

Puzzle Application
Cryptograms traditionally involve the Latin alphabet from A to Z, with each letter being turned into a different letter of the alphabet, with no overlaps. For example

ABCDEFGHIJKLMNOPQRSTUVWXYZ ↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓ QWERTYUIOPASDFGHJKLZXCVBNM

However, cryptograms are not required to include all letters in their text, and due to the infrequency of certain letter, often will neglect to include letters like J, Q, or X. This doesn't mean that the cipher is incomplete, simply that the solver will not always be able to determine the entire cipher themselves. In some cases, this is played into by the puzzle, purposefully leaving out certain letters from its text, or creating lipograms that leave out only one, allowing solvers to determine the missing cipher letter by process of elimination.

Some cryptograms will choose to double-up on representation, allowing one letter to represent multiple letters in the plaintext, or have certain letters represent themselves in the ciphertext. In these cases, non-hunt puzzles will often include these notes in their rules, while hunt puzzles may turn that into the 'aha moment' for the puzzle.

Non-Alphabetical Substitution
Cryptograms are very common within puzzle hunts, but the most notable ones tend to avoid using letters entirely. Cryptograms are notable, especially compared to alphanumeric substitution ciphers, in that any set of 26 things regardless of their relation to the English alphabet can be used to encode it, allowing cryptograms to range from the traditional (using letters to represent other letters) to the esoteric (using street signs to represent letters, for example).

This freedom of representation can sometimes be very successful, particularly if the things being used to represent letters are sufficiently interesting or dynamic. However, cryptograms whose only gimmicks are that they're represented by symbols or images can often fall flat, as static replacements are essentially just fancier versions of an alphabetical substitution. As long as solvers assign one of the 26 letters to each of symbols, they can just solve it like a normal cryptogram. While this is technically true of the more dynamic ones, such as someone using musical notes to represent letters, the extra interest generated by the unique presentation is more likely to carry it to success.

Cryptolists
Cryptolists are a subset of cryptograms, where a series of words or phrases sharing a common characteristic are encoded using the same cipher. These are distinct from most other cryptograms, which tend to encode full sentences rather than disconnected words or short phrases.

Played Straight

 * - A pangrammatic cryptogram, presented multiple times with different ciphers. Despite the puzzle, the actual cryptogram is fairly straightforward (if a bit tricky due to the pangrammatic nature)
 * - A cryptogram word search, in which the entire grid has been encoded using a particular cipher. Thanks to some entries having unique letter patterns, solvers can easily break in and decode the text fairly quickly.

Notable Twists

 * - Called 'The World's Most Beautiful Substitution Cipher' by the author, this puzzle involves videos of a couple performing some West Coast Swing, with each move/figure performed indicating a particular letter. Across the three videos, they can be used to decode what the cipher is, and determine the final answer.
 * - A cryptogram crossword (already solved), but with colors instead of letters. Notably, . Thankfully, all of the clues are still present (if unsorted), so solvers don't have to go in completely blind.
 * - An audio-based cryptogram that actually provides the key for solvers, in a way. Each letter is represented by an audio clip of the word 'radio', taken from various songs. Below the cryptogram is a series of pictures, each marked with a letter,.