There are 4,096 idols to collect. Each idol comes in 4 colors, bronze, silver, gold and diamond totaling the possible idols to get as 16,384. The algorithm in the game defaults to have the next idol that appears be one that you have not collected yet. You can collect idols by punching them when you see them. Most often they are found on stumps and columns, but sometimes imps are carrying them in the sky. Idols are not to be confused with statues, which are smaller, skinny items of various design also found on stumps and columns. You can view the idols that you have collected in the Punch Stats section of the main page. With update 1.1, Idols are now listed with names next to them. The names correspond to the appearance of the Idol (see example picture below).
Regular Idols tend to have a three word name:
The first word relates to the head, the second word relates to the eyes, and the third word relates to the mouth.
There are 16 Pure Idols in the game. They are associated with specific names like:
If you wish to unlock the achievment for collecting all 16 pure idols, you should probably not buy the silver/gold/diamond idol upgrades, since this will multiply the average number of idols you will have to collect by almost 2/3/4.