Record a log of your terminal session

How can we record everything we type in the terminal and all the output produced into a file? There is a command named script that can be used for this purpose. Just type script and everything will be recorded, not only the commands, but also the outputs. Once finished, type exit to end the recording session.

bash-3.2$ script my_history_April28_2015
Script started, output file is my_history_April28_2015
….
bash-3.2$ exit
exit
Script done, output file is my_history_April28_2015