I'm not sure I understand it from the description that I read, but I believe the Zodiac cipher to be a pretty simple transposition cipher applied to a simple substitution cipher containing complications due to garbage phrases inserted to fool statistical analysis.

Transposition ciphers alone simply scramble the order of their input (the plaintext). Substitution ciphers alone leave the characters in their original positions, but replace each plaintext character by a substitute character from the ciphertext alphabet.

In general, transposition ciphers are solved by using language frequencies and especially frequencies of letter tuples that appear in the text. For example, "t" is often followed by "h" and "q" is almost always followed by "u" and then a vowel. If a "t" is seen in the ciphertext of a transposition cipher, the cryptographer naturally looks for letters often on one side or the other of "t" and makes sample decipherment of the ciphertext based on the possibilities. Seeing a "q" often leads right away to a fruitful path to decrypting a simple transposition cipher.

There are countless transposition ciphers, and some are much more difficult to unravel. The Zodiac cipher appears to use a simple one, but some transposition ciphers can be very difficult to solve with short messages of under 1000 characters.

However, notice that the aforementioned techniques can't be used to solve the Zodiac transposition. The characters in the ciphertext are substitutes for the true characters appearing in the plaintext. This is an example of a substitution cipher. (The fact that the characters are little graphics is of no import and reveals the Zodiac author to be unaware of cryptographic principles.) This means that even if a "q" appears in the plaintext we can't directly use that fact to unravel the transposition step.

Furthermore, short substitution based ciphertexts are solved by looking at digram, trigram, and word frequencies when figuring out which ciphertext character corresponds to which plaintext character. A transposition cipher separates these digrams, trigrams and words; a transposition applied after even a simple substitution results in a code much harder to solve than a substitution or transposition alone.

Especially with the aid of computers, these ciphers can be attacked. I'm not aware of the details that the Zodiac cryptographers used. One way of proceeding would be to use properties of natural language letter frequencies. Low frequency letters tend to appear next to vowels, which are higher frequency. Using properties like this, we can detect when we may have found the inverse of the transposition step. Removing the transposition will leave a ciphertext that "looks" like an ordinary simple substitution cipher with low frequency symbols staying away from each other and touching certain high frequency symbols.

With the aid of statistics, we can reverse the transposition step. Perhaps there are a few dozen or even hundreds of possibilities that look statistically feasible for this step. These possibilities can then be attacked with powerful methods that solve simple substitutions.

Peak Hacker News right here ^.

There was this artist's puzzle (which unlocked a bitcoin address) I was working on pretty hard for about a month or so and after it was solved it also seemed 'rather simple'. Turned out there was only one missing piece of information between my attempts and the actual solution which, in hindsight, was pretty obvious.

Of course it seems easy after they tell you how its done.

The cipher is very hard to break by small teams of amateur cryptologists. Considering that it is, in a very simplified form, a monoalphabetic cipher combined with fancy transposition, I'd bet even the poorest nation states could break it easily but would not comment about it to avoid leaking its cryptanalysis methods and capabilities.