Left      Right      Description and pseudocode
===============================================================
Any       undef      check whether Any is undefined
               like: !defined Any

Any       Object     invoke ~~ overloading on Object, or die

Right operand is an ARRAY:

Left      Right      Description and pseudocode
===============================================================
ARRAY1    ARRAY2     recurse on paired elements of ARRAY1 and ARRAY2[2]
               like: (ARRAY1[0] ~~ ARRAY2[0])
                       && (ARRAY1[1] ~~ ARRAY2[1]) && ...
HASH      ARRAY      any ARRAY elements exist as HASH keys
               like: grep { exists HASH->{$_} } ARRAY
Regexp    ARRAY      any ARRAY elements pattern match Regexp
               like: grep { /Regexp/ } ARRAY
undef     ARRAY      undef in ARRAY
               like: grep { !defined } ARRAY
Any       ARRAY      smartmatch each ARRAY element[3]
               like: grep { Any ~~ $_ } ARRAY

Right operand is a HASH:

Left      Right      Description and pseudocode
===============================================================
HASH1     HASH2      all same keys in both HASHes
               like: keys HASH1 ==
                        grep { exists HASH2->{$_} } keys HASH1
ARRAY     HASH       any ARRAY elements exist as HASH keys
               like: grep { exists HASH->{$_} } ARRAY
Regexp    HASH       any HASH keys pattern match Regexp
               like: grep { /Regexp/ } keys HASH
undef     HASH       always false (undef can't be a key)
               like: 0 == 1
Any       HASH       HASH key existence
               like: exists HASH->{Any}

Right operand is CODE:

Left      Right      Description and pseudocode
===============================================================
ARRAY     CODE       sub returns true on all ARRAY elements[1]
               like: !grep { !CODE->($_) } ARRAY
HASH      CODE       sub returns true on all HASH keys[1]
               like: !grep { !CODE->($_) } keys HASH
Any       CODE       sub passed Any returns true
               like: CODE->(Any)

Right operand is a Regexp:

Left      Right      Description and pseudocode
===============================================================
ARRAY     Regexp     any ARRAY elements match Regexp
               like: grep { /Regexp/ } ARRAY
HASH      Regexp     any HASH keys match Regexp
               like: grep { /Regexp/ } keys HASH
Any       Regexp     pattern match
               like: Any =~ /Regexp/

Other:

Left      Right      Description and pseudocode
===============================================================
Object    Any        invoke ~~ overloading on Object,
                     or fall back to...

Any       Num        numeric equality
                like: Any == Num
Num       nummy[4]    numeric equality
                like: Num == nummy
undef     Any        check whether undefined
                like: !defined(Any)
Any       Any        string equality
                like: Any eq Any