The philosopher Nick Bostrom published a paper in 2003 that many people initially read as science fiction. He argued, with formal logical rigour, that one of three things must be true: almost all civilisations go extinct before developing the ability to run realistic computer simulations of minds; almost all civilisations that reach that ability choose not to run such simulations; or we are almost certainly living in a simulation right now. This is called the Simulation Argument, and it has refused to go away.
Why the argument has force
The logic is uncomfortably clean. If any civilisation in the history of the universe ever developed the ability to run detailed ancestor simulations and ran many such simulations, then the simulated minds would vastly outnumber the 'real' ones. Simple probability then says you should expect to be in a simulation. The argument doesn't require anything supernatural. It just requires that computing power continues to grow and that some civilisation somewhere eventually becomes sufficiently advanced.
What physics might be telling us
Some features of physical reality look more like computation than classical physics would predict. The fact that the universe appears to have a minimum possible resolution at the Planck scale. The quantisation of energy. The strange way quantum systems seem to only commit to definite states when measured. None of this proves simulation. But it's curious that the universe looks more like a computed system than a purely analogue one.
Why it keeps mattering anyway
The reason the simulation hypothesis won't leave the cultural conversation is that it reframes one of the oldest human questions: what is real? It takes that question out of purely philosophical or religious territory and puts it in a framework that people trained in science and technology find it hard to simply dismiss.
Whether or not we're simulated, the question of reality's ultimate nature turns out to be just as open as it ever was.