Your try, \\.+?\.pdf matches:

1. A backslash
2. As little anything as is possible, nongreedy
3. a dot and then pdf

I think what you would want, instead of matching As little anything as is possible, nongreedy you want Anything except a backslash.

More likely, you just want basename from File::Basename.

Right. I realize why the regexp I tried doesn't work. The solution can't be anything except a backslash, it has to be something like the last set of characters that isn't preceded by a backslash. I realize I could do this with a module, splitting on backslashes then taking the last element, etc., but I want to do it with a regexp if I can.

I'm not sure what you mean by

The solution can't be anything except a backslash, it has to be something like the last set of characters that isn't preceded by a backslash.

The following will match the last sequence of non-backslash characters in your string, which is what you seem to want:

m![^\\]+\.pdf$!;
[download]

Anchoring the match makes sure you get the filename path, and the character set negation makes sure you get nothing with a backslash in it.

qr{
    [^\\/]+  # one or more non-slash characters
    $        # the end of the string
}x
[download]

$a = "C:\Communication...";

($b) = $a =~ m/.*\\(.*)/;
[download]

To perform operations on filenames,
see this core module File::Spec

#!/usr/bin/perl -w
use  strict;
use File::Spec;

my $path = q{C:\Communications%20by%20Date\1995\19950711%20UBL%20An%20
+Open%20Letter%20to%20King.pdf}; 

my ($volume,$directories,$file) = File::Spec->splitpath( $path );
print $file, "\n";

__END__
Output : 
19950711%20UBL%20An%20Open%20Letter%20to%20King.pdf
[download]

hth,
PooLpi