There are two ways to approach Swayambhunath Temple, but by far the most atmospheric is the stone pilgrim stairway that climbs the eastern end of the hill. Constructed by King Pratap Malla in the 17th century, this steep stone staircase is mobbed by troops of rhesus macaques, who have made an artform of sliding down the steep handrails. A word of advice: keep foodstuffs out of sight of these simian hoodlums!
From a collection of brightly painted Buddha statues at the bottom of the hill, the steps climb past a series of chaitya and bas-reliefs, including a stone near the entrance showing the birth of the Buddha, with his mother Maya Devi grasping a tree branch. You can often see Tibetan astrologers reading fortunes here. At the top, the steps are lined with pairs of Garudas, lions, elephants, horses and peacocks: the ‘vehicles’ of the Dhyani Buddhas. Near the end of the climb is the ticket office (there’s another one at the western entrance, near the tourist bus park). When you reach the top, remember to walk around the stupa in a clockwise direction.