How can I gzip standard in to a file and also print standard in to standard out?

Another way (assuming a shell like bash or zsh):

echo "hey hey, we're the monkees" | tee >(gzip --stdout > my_log.gz)

The admittedly strange >() syntax basically does the following:

• Create new FIFO (usually something in /tmp/)
• Execute command inside () and bind the FIFO to stdin on that subcommand
• Return FIFO filename to command line.

What tee ends up seeing, then, is something like:

tee /tmp/arjhaiX4

All gzip sees is its standard input.

For Bash, see man bash for details. It's in the section on redirection. For Zsh, see man zshexpn under the heading "Process Substitution."

As far as I can tell, the Korn Shell, variants of the classic Bourne Shell (including ash and dash), and the C Shell don't support this syntax.

echo "hey hey, we're the monkees" | tee /dev/tty | gzip --stdout > my_log.gz

As pointed out in the comments, /dev/stdout might work better than /dev/tty in some circumstances.

Have a nice cup of tee!

The tee command copies standard input to standard output and also to any files given as arguments. This is useful when you want not only to send some data down a pipe, but also to save a copy

As I'm having a slow afternoon, here's some gloriously illustrative ascii-art...

           +-----+                   +---+                  +-----+  stdin ->   |cmd 1|    -> stdout ->   |tee|   ->  stdout  -> |cmd 2|           +-----+                   +---+                  +-----+                                       |                                       v                                     file

As greyfade demonstrates in another answer the 'file' need not be a regular file, but could be FIFO letting you pipe that tee'd output into a third command.

           +-----+                   +---+                  +-----+  stdin ->   |cmd 1|    -> stdout ->   |tee|   ->  stdout  -> |cmd 2|           +-----+                   +---+                  +-----+                                       |                                       v                                     FIFO                                       |                                       v                                    +-----+                                    |cmd 3|                                    +-----+