Cryptarithms come in three types: alphametic, digimetic and skeletal division. The main premise of a cryptarithm is that the numbers in some type of arithmetic expression are replaced with something else, and the goal is to figure out the original digits.
An alphametic cryptarithm is where the digits in the expression are replaced with letters. The first modern alphametic is attributed to Henry Dudeney where SEND+MORE=MONEY has the solution 9567+1085=10652. A digimetic cryptarithm is where the numerical digits are replaced with other numerical digits. Skeletal division cryptarithms are arguably the most complex and are where a long division problem is set up but all or some of the numbers are replaced with symbols, such as asterisks.