The theological situation was the "standard" one of a Ban and a Fall. The Númenóreans, despite having been granted a longer lifespan than other, humans, nevertheless had to remain mortal. They had also been ordered not to sail West to the Undying Lands (Valinor). After awhile (perhaps inevitably, as their power and wealth grew) the Númenóreans began to envy the Elves and to yearn for immortality themselves (so as to enjoy their situation longer). They managed to convince themselves that physical control of the Undying Lands would somehow produce this result (it would not have); however, they also retained sufficient wisdom not to attempt any such foolish action. Significantly, the more obsessed they became with death the more quickly it came as their lifespans steadily waned.
Near the end of the Second Age King Ar-Pharazôn the Golden pridefully challenged Sauron for the mastery of Middle-earth. The Númenóreans won the confrontation and took Sauron to Númenor as a prisoner. Still wielding the One Ring, he swiftly gained control over most of the Númenóreans (except for the Faithful and their leaders, Amandil and his son Elendil). As King Ar-Pharazôn's death approached ("he felt the waning of his days and was besotted by fear of death"; RK, p. 317) Sauron finally convinced him by deception to attack Valinor. This was a mistake. A great chasm opened in the Sea and Númenor toppled into the abyss. (Tolkien had a recurrent dream about this event; in LotR he gave it to Faramir, who described it in "The Steward and the King".)