The synopsis for Unicode::Collate does a reasonable job of setting the stage, but there is a nice discussion in chapter 6 of Programming Perl (the camel book), 4th edition as well. You might also look at the Unicode Technical Standard #10: Unicode Collation Algorithm.

Here's a brief example of doing comparisons at a lower (more relaxed) level using Unicode::Collate.

use strict;
use warnings FATAL => 'utf8';
use utf8;

use Unicode::Collate;
binmode STDOUT, ':encoding(UTF-8)';

my( $x, $y, $z ) = qw( α ά ὰ );

my $c = Unicode::Collate->new;

print "\nStrict collation rules: Level 4 (default)\n";
print "\t cmp('α','ά'): ", $c->cmp( $x, $y ), "\n";
print "\t cmp('ά','ὰ'): ", $c->cmp( $y, $z ), "\n";
print "\t cmp('α','ὰ'): ", $c->cmp( $x, $z ), "\n";

my $rc = Unicode::Collate->new( level => 1 );

print "\nRelaxed collation rules: Level 1\n";
print "\t cmp('α','ά'): ", $rc->cmp( $x, $y ), "\n";
print "\t cmp('ά','ὰ'): ", $rc->cmp( $y, $z ), "\n";
print "\t cmp('α','ὰ'): ", $rc->cmp( $x, $z ), "\n\n";

And the output...

Strict collation rules: Level 4 (default)
	 cmp('α','ά'): -1
	 cmp('ά','ὰ'): -1
	 cmp('α','ὰ'): -1

Relaxed collation rules: Level 1
	 cmp('α','ά'): 0
	 cmp('ά','ὰ'): 0
	 cmp('α','ὰ'): 0

And if the reason for doing comparisons is to handle sorting, Unicode::Collate does that too (you don't need to explicitly use Perl's core sort).