Launch a background process and check when it ends

The key is the "wait" command:

#!/bin/bash

/my/process &
/another/process &
wait
echo "All processes done!"

With wait you can have the granularity you need:

sleep 1 &
PID1=$!
sleep 2 &
PID2=$!

wait $PID1
echo 'PID1 has ended.'
wait
echo 'All background processes have exited.'

Here is one way to do it:

launch backgroundprocess &
PROC_ID=$!

while kill -0 "$PROC_ID" >/dev/null 2>&1; do
    echo "PROCESS IS RUNNING"
done
echo "PROCESS TERMINATED"
exit 0