The Borobudur had been on my top wish list to see WHS for a long time. Finally in May 2016 it was time. I visited most of the Indonesian WHS.
Not going into the history but a few practical things. I suggest going on a sunrise tour. This is simply amazing (see photos on the link). After the sunrise you have time to explore the complex; that's the time the groups come in too. So you have less tourists. Much better for photography.
The sunrise was amazing. First the clouds turn purple-orange-red when the sunrises, but still behind the Merapi volcano. Then it gets boring for 20 minutes; don't leave! Then, you will see the sun coming from behind the Merapi and the sky again turns orange-magenta! It's magical! See my photos on the link.