All of these are valid SQL exppressions.  Where I have a number you can also use a field name.
 
Modular Arithematic mod(29,3)
Normal Math 3+(2*4)
Binary OR 27 | 31
Binary AND 27 & 31
Binary LEFTSHIFT 27 << 1
Binary RIGHTSHIFT 27 >> 1
Binary INVERSION ~4
Count the set bits BIT_COUNT(4)
Logical AND age = 10 && age < 20
Logical OR age = 3 || age = 2
Logical NOT not age = 3
Equality =
Less than  <
Greater than >
Less than or equal to <=
Greater than or equal to >=
Not equal to (version 1) !=
Not equal to (null is null) <=>
Test for nullness pop IS NULL, ISNULL(pop)
Test for non-nullness pop IS NOT NULL
Range check pop BETWEEN 3 AND 7
Set inclusion pop in (3, 4, 17)
Set exclusion pop not in (3, 4, 17)
Interval checking INTERVAL(23, 1, 10, 11, 20, 21, 30)
Intervals must be in order
Regular expression string functions
(SQL style)
"David" LIKE "_avid"
 "%" means any number of chars (including zero)
_ means any one char
Relular expression string functions
(Unix style)
David RLIKE ".u."
doesn't always work for me
If IF(age > 10, "adult", "child")
Absolute value ABS(pop - 1000)
Sign SIGN(pop - 1000)
Rounding to closest int ROUND(pop / 1000, 2)
A random number RAND()
Leftmost part of a string LEFT("Hello", 4)
right also works
Middle part of a string MID("Hello", 3, 2)
starts counting at 1
Sounds like SOUNDEX("fil") = SOUNDEX("phil")

Rules for performing comparisons

MySQL performs comparisons using the following rules:

    If one or both arguments are NULL, the result of the comparison is NULL, except for the <=> operator.
    If both arguments in a comparison operation are strings, they are compared as strings.
    If both arguments are integers, they are compared as integers.
    Hexadecimal values are treated as binary strings if not compared to a number.
    If one of the arguments is a TIMESTAMP or DATETIME column and the other argument is a constant, the constant is converted to a timestamp
    before the comparison is performed. This is done to be more ODBC-friendly.
    In all other cases, the arguments are compared as floating-point (real) numbers.