Rameswaram is where the two great streams of Hindu devotion meet without either giving way, and the arrangement is stated in the temple's founding story.
A Vaishnava reason for a Shaiva temple
The Ramayana supplies the account: Rama, having killed Ravana, incurs the guilt of killing a Brahmin, and worships Shiva here to expiate it. He sends Hanuman to fetch a linga from Kailasa; Hanuman is delayed, and Sita fashions one from sand so the rite can proceed at the auspicious moment. Both lingas are said to be in the temple, and the sand one is worshipped first, by Rama's instruction.
The result is that one of the twelve jyotirlingas, the principal shrines of Shiva, exists because the avatar of Vishnu needed to worship there. The story is doing deliberate work: it makes the two traditions dependent on each other rather than rivals, and it is why Rameswaram appears both among the jyotirlingas and among the four Char Dham.
The corridor
The temple's architectural fame rests on its corridors, which run to something over a kilometre in total, the longest in India, lined with more than a thousand carved pillars, each different, receding in a perspective that has been photographed since photography reached India.
They were built late: by the Sethupathi rulers of Ramnad between 1763 and 1795. The great corridor is younger than the United States.
The twenty-two wells
Pilgrims bathe at twenty-two tirthas within the precinct before darshan, each said to correspond to an arrow in Rama's quiver. The water is drawn and poured over the pilgrim at each in turn, and the circuit is a soaking, cheerful, thoroughly physical business that takes a good while.
Who paid for it
The patronage is unusually varied for a South Indian temple. Parts may go back to the eleventh or twelfth century. Kings of Jaffna in Sri Lanka renovated the sanctum around 1400, and earlier Sri Lankan rulers contributed, which is worth noting given that the temple commemorates a war against Lanka. The island visible across the strait is the one Rama is said to have invaded, and its rulers helped rebuild the shrine.
The Tamil Nadu endowments department administers it now.