SQL operators include arithmetic, comparison, and logical operators. Arithmetic operators are used to perform math operations like addition and subtraction. Comparison operators compare values, returning TRUE if the conditions are met. Logical operators combine multiple conditions and can negate outputs. Range and pattern matching operators also allow searching for values within a specified range or matching a pattern using wildcards. The document provides examples of using various SQL operators like BETWEEN, LIKE, and arithmetic/comparison operators to search a sample student table.