When Jews began moving back into the territory in the 1800s the tenseness increased between the two religions. Jews come to the wall from all over the world. Many write prayers and messages on paper and stick them between the cracks. The men wear either a hat or yarmulka to show respect. At the wall you can hear some of them wailing or crying for the loss of their great temple.
Many events take place at the wall such as religious gatherings and celebrations.
Today the area is under Jewish control since the 1967 Arab-Israeli War when Jerusalem captured Jordan. Maybe quick body frisks or opening bags, etc. Remember the Wailing Wall is considered a place of worship. Don't go in short shorts and tank tops. Show respect and remember that many will be there praying.