Watch out for the difference of priority between 'and vs &&' or '|| vs or':
<?php
$bool = true && false;
var_dump($bool); // false, that's expected

$bool = true and false;
var_dump($bool); // true, ouch!
?>
Because 'and/or' have lower priority than '=' but '||/&&' have higher.

Note that ?? has a low priority, so this can lead to unexpected results:

$a=[];
$a['aa']??'not set' 
--> not set (as expected)

but
"lets see if it is set".$a['aa']??'not set'
--> notice; undefined index aa
--> lets see if it is set

so you need to use parenthesis
"lets see if it is set".($a['aa']??'not set')

If you've come here looking for a full list of PHP operators, take note that the table here is *not* complete. There are some additional operators (or operator-ish punctuation tokens) that are not included here, such as "->", "::", and "...".

For a really comprehensive list, take a look at the "List of Parser Tokens" page: http://php.net/manual/en/tokens.php

Beware the unusual order of bit-wise operators and comparison operators, this has often lead to bugs in my experience. For instance:

<?php if ( $flags & MASK  == 1) do_something(); ?>

will not do what you might expect from other languages. Use

<?php if (($flags & MASK) == 1) do_something(); ?>

in PHP instead.

An easy trick to get the result of the left shift operation (<<), e.g.

15 << 2 = 15 * (2*2) = 60

15 << 3 = 15 * (2*2*2) = 120

15 << 5 = 15 * (2*2*2*2*2) = 480

and so on...

So it's:

(number on left) multiplied by (number on right) times 2.

The same goes for the right shift operator (>>), where:

(number on left) divided by (number on right) times 2 e.g.

15 >> 2 = (15/2)/2 = 7/2 = 3 (use floor values if result is in decimals).

35 >> 3 = (((35/2)/2)/2 = (17/2)/2 = 8/2 = 4

Using cast and ternary operator can be unclear,
(Useful to know with: declare(strict_types = 1) ). 
<?php
$num_str="5";

$i1 = (int)  isset($num_str) ? $num_str : 0;
$i2 = (int) (isset($num_str) ? $num_str : 0);
var_dump($i1);
var_dump($i2);
?>
Output:
string(1) "5"
int(5)

<?php 
// Another tricky thing here is using && or || with ternary ?:
$x && $y ? $a : $b;  // ($x && $y) ? $a : $b;

// while:
$x and $y ? $a : $b;  // $x and ($y ? $a : $b);

?>

//incorrect
$a = true ? 0 : true ? 1 : 2; // (true ? 0 : true) ? 1 : 2 = 2
//Unparenthesized `a ? b : c ? d : e` is not supported. Use either `(a ? b : c) ? d : e` or `a ? b : (c ? d : e)` 
//correct
$a = (true ? 0 : true) ? 1 : 2; // (true ? 0 : true) ? 1 : 2 = 2

==> correction documentation.