Prima facie, valuing a longevity-contingent claim that provides guaranteed income-for-life should be a relatively straight forward operation. One selects a mortality basis with a proper discount curve and the remainder is left to expectations. And yet, history is strewn with examples of mispriced annuities. From early attempts by the English King Henry VIII to securitize cash flows from the dissolution of the monasteries in the 16th century, to European tontines in the 17th and 18th centuries and of course North American variable annuity companies who teetered on the precipice of bankruptcy in the early 21st century, it seems annuities can be a very tricky business. Motivated by these examples and recent controversies, in this talk I will review the pricing of plain, compound and decorative annuities, discuss the economic rationale for their existence and conclude with some observations on why Mother Nature would prefer that retirees pool longevity risk.