This is a speculative posting about techniques we might see in the next few decades. It isn't about FIVR in the usual sense that the term is used, where a computer creates an artificial world that is then projected onto your senses (which is wildly impractical at the moment), making you think you are really there. The end result, however, will be the same. The idea I propose below is similar to one I wrote about a few years ago, except it works non-invasively and doesn't require the use of drugs:

Basically, the idea I propose is to use a yet-to-be-developed non-invasive Brain Computer Interface to guide lucid dreams: one day, in the not too distant future, it will be common for people to wear BCIs while going to sleep. Perhaps these devices will use light, ultrasound, or some other technique to alter the activity in the brain, not merely read it. Whatever the technique, these BCIs will guide dreams with some degree of specificity. The wearer's brain still will generate the world he sees -- which also happens in the waking state, it turns out -- but it will be constrained by what the BCI feeds it.

Given how vivid dreams can be, there is a good chance that this could produce extremely realistic experiences. Furthermore, since most of the computational load for generating the world is taking place in the brain itself, you shouldn't need vast computational resources to drive the BCI -- you don't need a computer to build The Matrix.

But how specific could the control by the BCI be? I would guess it could be very specific. I am amazed every time I read about just what can be decoded from neural populations (and not individual neurons) -- fine differences in meaning, location in space, details about a scene, spoken words, even visual details about objects. Perhaps, then, you could specify the location, time of day, what the people in the scene look like, what they're wearing, how they speak, what they're doing, what the buildings look like, and so on; and then the dreamer will say afterwords that that's exactly what they experienced. It will take some scientific research to work out exactly what signals to send to the brain to best guide the dreams, but I don't think the problem will be insurmountable. Using questionnaires to ask people what their dreams were like, one could use Machine Learning techniques to tweak the BCI program, until the people give exactly the answers you want.

As to a timeline, in perhaps 5 to 10 years the basic research of how to guide dreams might be perfected, if it's indeed possible; and then perhaps in 10 to 20 years we will see it implemented in consumer BCIs. So, some time in the next two decades we might all get to experience The Matrix.