People tend to assume that sleeping straight through the night for 8 hours is what is meant, because it seems so normal to all of us. However, the rules aren't actually tied to that. The need for sleep and the need for long rests are two separate things.
Long rests can be taken without any sleep at all.
No, they cannot. At least not as of the August 2017 errata to the resting rules, which changed the wording of the rules for a long rest from:
pre-errata rules said:
A long rest is a period of extended downtime, at least 8 hours long, during which a character sleeps or performs light activity: reading, talking, eating, or standing watch for no more than 2 hours.
to:
post-errata rules said:
A long rest is a period of extended downtime, at least 8 hours long, during which a character sleeps for at least 6 hours and performs no more than 2 hours of light activity, such as reading, talking, eating, or standing watch..
The purpose of this errata was to clarify the ambiguity in the wording, “sleeps or performs light activity: reading, talking, eating, or standing watch for no more than 2 hours,” which could be interpreted to mean that you can spend the entire rest sleeping and/or performing light activity such as eating, as long as or performing light activity, provided you do not stand watch for more than two hours. The new wording, “sleeps for at least 6 hours and performs no more than 2 hours of light activity, such as reading, talking, eating, or standing watch.” makes the intent clear: reading, talking, eating, and standing watch are all considered light activity, and you can spend no more than 2 hours of a long rest performing such activity.
Under this new wording, it is abundantly clear that a character does in fact need to sleep for at least a total of 6 hours during a single 8-hour period in order to gain the benefits of a long rest. Those 6 hours do not need to be consecutive, but the 8 hours do. So you could, for example, sleep for 3 hours, stand watch for 2 hours, then sleep for 3 more hours. Or you could sleep for 2 hours, stand watch for 1 hour, go back to sleep for 2 more hours, stand watch for another hour, and sleep for another 2 hours. But you could not sleep for 5 hours and stand watch for 3 hours, nor could you sleep for 6 hours and then go back to adventuring. At least 8 hours must be spent doing some combination of sleeping and light activity that totals at least 6 hours of sleep and no more than 2 hours of light activity, with no more than a 1-hour interruption, otherwise it is not a long rest.