Show yesterday's date:

$ date -d yesterday
$ date -d yesterday +%Y-%m-%d

Show the UNIX timestamp:

$ date +%s
$ date --utc +%s
$ date -d yesterday --utc +%s

Convert a date string to timestamp:

function date2stamp () {
        date --utc --date "$1" +%s
} 

Convert a timestamp to a date string:

function stamp2date () {
        date --utc --date "1970-01-01 $1 sec" "+%Y-%m-%d %T"
} 

Calculate a date difference:

function dateDiff () {
         case $1 in
                 -s) sec=1; shift;;
                 -m) sec=60; shift;;
                 -h) sec=3600; shift;;
                 -d) sec=86400; shift;;
                 *) sec=86400;;
         esac

         dte1=$(date2stamp $1)
         dte2=$(date2stamp $2)
         diffSec=$((dte2-dte1))
         if ((diffSec < 0)); then abs=-1; else abs=1; fi
         echo $((diffSec/sec*abs))
 } 

Reference:

• Simple date and time calulation in BASH 
• How to format date for display or to use in a shell script