Scope of environment variables in shells and shell scripts

A environment variable defined in a shell (or a shell script) stays defined everywhere, including inside new shells (or shell scripts) executed within the shell, until the shell (or the shell script) terminates or the variable gets unset explicitly. E.g.

script1.sh contains:

export VAR1=testing
bash script2.sh

script2.sh contains:

echo $VAR1

Then executing script1.sh gives the following:

bash-3.00$ bash script1.sh 
testing
bash-3.00$ echo $VAR1

bash-3.00$ echo $UNDEFINED_VAR

bash-3.00$