max

The simplest way to get around the fact that max() won't give the key is array_search:
<?php
$student_grades = array ("john" => 100, "sarah" => 90, "anne" => 100);
$top_student = array_search(max($student_grades),$student_grades); // john
?>

This could also be done with array_flip, though overwriting will mean that it gets the last max value rather than the first:
<?php
$grades_index = array_flip($student_grades);
$top_student = $grades_index[max($student_grades)]; // anne
?>

To get all the max value keys:
<?php
$top_students = array_keys($student_grades,max($student_grades)); // john, anne
?>

Watch out after PHP 8.0!
Sample code:
<?php
echo max(0,'hello');
?>

Before PHP 8.0 will return int(0) but since PHP 8.0 above code returns string("hello")!!

max() (and min()) on DateTime objects compares them like dates (with timezone info) and returns DateTime object.
<?php 
$dt1 = new DateTime('2014-05-07 18:53', new DateTimeZone('Europe/Kiev'));
$dt2 = new DateTime('2014-05-07 16:53', new DateTimeZone('UTC'));
echo max($dt1,$dt2)->format(DateTime::RFC3339) . PHP_EOL; // 2014年05月07日T16:53:00+00:00
echo min($dt1,$dt2)->format(DateTime::RFC3339) . PHP_EOL; // 2014年05月07日T18:53:00+03:00
?>

It works at least 5.3.3-7+squeeze17

max(null, 0) = null
max(0, null) = 0

Notice that whenever there is a Number in front of the String, it will be used for Comparison.
<?php
 max('7iuwmssuxue', 1); //returns 7iuwmssuxu
 max('-7suidha', -4); //returns -4
?>

But just if it is in front of the String
<?php
 max('sdihatewin7wduiw', 3); //returns 3
?>

With modern PHP versions supporting the array spread operator for function arguments, it's tempting to call max() like this:
<?php
function stuff(): iterable {
 // This function might yield 0, 1 or n values.
}
$foo = max(...stuff());
?>

However, this is dangerous if you cannot guarantee that your generator yields **minimum** two values.
The gotcha here is that when max() receives a single argument, it must be an array of values. (When the generator doesn't yield any values, max() will throw an ArgumentCountError.)
If you can guarantee that your generator yields at least one value, then it's safe to call max by relying on the aforementioned array expectation:
<?php
function stuff(): iterable {
 // This function will yield 1...n values.
}
// Note that here the generator is first read into an array.
$foo = max([...stuff()]);
?>

If the array is empty, max() will throw a ValueError.
The added burden is that faulty code could appear to appear to function just fine but fails at random, probably causing a lot of head-scratching at first.

Regarding boolean parameters in min() and max():
(a) If any of your parameters is boolean, max and min will cast the rest of them to boolean to do the comparison.
(b) true > false
(c) However, max and min will return the actual parameter value that wins the comparison (not the cast).
Here's some test cases to illustrate:
1. max(true,100)=true
2. max(true,0)=true
3. max(100,true)=100
4. max(false,100)=100
5. max(100,false)=100
6. min(true,100)=true
7. min(true,0)=0
8. min(100,true)=100
9. min(false,100)=false
10. min(100,false)=false
11. min(true,false)=false
12. max(true,false)=true

I had several occasions that using max is a lot slower then using a if/then/else construct. Be sure to check this in your routines!
Ries

Note that max() can compare dates, so if you write something like this:
<?php
$dates = array('2009-02-15', '2009-03-15');
echo max($dates);
?>

you will get: 2009年03月15日.

Matlab users and others may feel lonely without the double argument output from min and max functions.
To have the INDEX of the highest value in an array, as well as the value itself, use the following, or a derivative:
<?php
function doublemax($mylist){
 $maxvalue=max($mylist);
 while(list($key,$value)=each($mylist)){
 if($value==$maxvalue)$maxindex=$key;
 }
 return array("m"=>$maxvalue,"i"=>$maxindex);
}
?>

In response to: keith at bifugi dot com
If you want to find the specific key(s) that match the maximum value in an array where the values may be duplicated, you can loop through and perform a simple check:
<?php
# Example Array
$a = array(
 'key1' => 100,
 'key2' => 90,
 'key3' => 100,
 'key4' => 90,
);
# First get the maximum value
$max = max($a);
# Create a new array containing all keys which have the max value
foreach($a as $key => $val) { 
 if($val === $max) $b[] = $key;
}
# If you want a string list, just do this
$b = implode(' ', $b);
?>

This produces consistent results and will scale well in terms of performance, whereas functions like array_search and array_flip can lead to degraded performance when dealing with large amounts of data.

Be aware if a array like this is used (e.g. values from a shopping cart):
<?php
Array
(
 [0] => 142,80
 [1] => 39,27
 [2] => 22,80
 [3] => 175,80
)?>
The result will be: 39,27 and not - as expected - 175,80
So, to find the max value, use integer only like:
<?php
Array
(
 [0] => 14280
 [1] => 3927
 [2] => 2280
 [3] => 17580
)?>
and you will get the correct result: 17580