In bash, every command in a pipeline is executed in a subshell. In zsh, the last command in a pipeline is executed in current shell. For example, the following code

var="before"
echo "after" | read var
echo $var

will print before in bash, but after in zsh.

In bash, you have to quote arguments in order to preserve white space:

# bash

function print_first_argument {
    echo "$1"
}

argument="has white space"
print_first_argument "$argument"

In Zsh, you don't need the quotes, because of different evaluation order:

# zsh

function print_first_argument {
    echo $1
}

argument="has white space"
print_first_argument $argument

When nothing matches a wildcard such as * in bash, it gets passed on as a literal * to the command, as if you had typed \*. However, zsh throws an error.

Bash:

duncan@K7DXS-Laptop-Arch:~/test$ echo *.txt
*.txt
duncan@K7DXS-Laptop-Arch:~/test$ touch abc.txt
duncan@K7DXS-Laptop-Arch:~/test$ echo *.txt
abc.txt
duncan@K7DXS-Laptop-Arch:~/test$ 

Zsh:

K7DXS-Laptop-Arch% echo *.txt   
abc.txt
K7DXS-Laptop-Arch% rm abc.txt 
K7DXS-Laptop-Arch% echo *.txt
zsh: no matches found: *.txt
K7DXS-Laptop-Arch% 

This is most noticeable in programs that use a literal *, such as find:

duncan@K7DXS-Laptop-Arch:~/test$ ls -R
.:
abc

./abc:
123.txt

Bash:

duncan@K7DXS-Laptop-Arch:~/test$ find -name *.txt
./abc/123.txt
duncan@K7DXS-Laptop-Arch:~/test$ 

Zsh:

K7DXS-Laptop-Arch% find -name *.txt
zsh: no matches found: *.txt
K7DXS-Laptop-Arch% find -name \*.txt
./abc/123.txt
K7DXS-Laptop-Arch% find -name '*.txt' # Notice single rather than double quotes
./abc/123.txt
K7DXS-Laptop-Arch% 

Global aliases

In bash, aliases can only be placed at the beginning of of a command, but zsh supports aliases anywhere. If you place the following line in your $ZDOTDIR/.zshrc

alias -g G=' | grep -i'

You can then run

cat haystack.txt G "needle"

Suffix aliases (Added in zsh 4.2.x)

Suffix aliases allow you to tell zsh to open files with specify a program to open files with certain extensions. Examples:

alias -s c="emacs"
alias -s php="vim"
alias -s java="$EDITOR"

Now in your shell, if you have a php file, file.php, and you run the command

file.php

It will automatically open file.php in vim.