When I was learning map and grep, it helped me to see the equivalent of them in normal perl code.

my @a = map { transformation($_) } @b;
# same as
my @a;
push @a, tranformation($_) for @b;
@a
[download]

And

my @a = grep { condition($_) } @b;
# same as
my @a;
for (@b) {
   push @b, $_ if condition($_);
}
@a
[download]

If you see yourself using one of those patterns, you can likely use map or grep instead.

And as a final note, you can use both without a block if you want to use only one expression:

my @even = grep $_ % 2 == 0, @numbers;
my @odd  = map $_ * 2 +1,    @numbers;
[download]

In particular that allows you to write

my @numbers = grep /^[0-9]+$/, @words;
[download]