Adding (and exporting) tags to pictures

I am trying to find a way to organize picture metadata in my Android phone. By default, it adds location and time data, so that the photos are easily searchable on the phone. I can also tag people and the software recognizes faces and suggests people name. Unfortunately, it seems that both people name and location data are not available when I donwload the photos on my computer. The metadata should be written in the photos in EXIF, IPTC and/or XMP format, so that other tools on my computer will recognize them. Also, I can only tag people when the software recognizes that there is a face, and many photos of people are not correctly recognize as such. Is there some way I can tag and organize pictures, storing the metadata correctly in the photos themselves?