By that I mean the ability for instance to charge a laptop or cellphone battery without plugging into the mains, or to run household appliances completely wirelessly, all power being transmitted through the air from some power station?
BTW I checked out the wiki on wireless power but am ashamed to say that most of it went straight over my head.
We have wireless power today. You can get a pad that you put your device on and it charges without you needing to plug the device in, if it’s designed for such a method. Long range wireless power is out of the question except for miniscule levels of power.
Here is a wireless charger for your cellphone or laptop. It receives power from a distant nuclear power station. But it only works during certain times of the day.
Cute, but to you use that you still need to plug your appliance into it to use the power. It’s no more wireless than, say, a standard diesel generator. The OP was specifically asking for “wireless” in the sense of there being no need to have a wire running from the appliance which consumes the power to the appliance which generates it.
Well then here you go: Samsung debuts solar-powered cell phone
No wires needed.
OK, I was being a little bit cute. But I was trying to illustrate the principle that it is possible to transmit energy from Point A to Point B wirelessly. You don’t get as much usable energy with either of these examples as you would really like. Perhaps you could do better using a laser or microwave beam, but you wouldn’t want somebody walking through the beam.
Wireless power is, and will remain for the forseeable future, a low power short distance affair. Put your cellphone down in a defined area, and it recharges.
If you try to transmit a lot of energy over a significant distance, it’s going to involve a lot of power loss, and is likely to be very dangerous to people. The amount of power needed to run a coffee maker would kill a person, easily. Now you’re trying to send that power wirelessly into my kitchen, to the coffee maker, where I’m going to be standing right next to the thing, holding the thing, and not getting myself fried. There’s no convenient insulator protecting me from the electrical energy, it’s flowing right through the air, right through me, to get to the appliance.
Plus you’d have to come up with some clever scheme to make sure that the energy was only going to the person who paid for it (or at least make anyone who intercepts it pay for it). I don’t know if we have a way of encrypting energy yet.
And that is not a problem if you’re a poor receptor for that form of energy and the coffee maker is a good one. All the things between the transmitter and the coffee-maker that is more similar to coffee-maker than to a human are much more problematic.
experiments have been done with low power locally; e.g. cell phone inside of a room. not very practical yet.
These are nitpicks but we’ve had wireless power for years. Microwave transmissions have been used for communications for decades. That technology is capable of transmitting a significant amount of power wirelessly but the costs and risks make it a bad choice. (Think roasted duck on the fly)
And the most common transformer design transmits power magnetically over a gap between coils. It has the added benefit of changing the voltage. That property is the reason your cordless toothbrush can charge while sitting in it’s base even without metal contacts.
You could do that with sufficiently-narrowly targeted power transmission. Your device would register its location and the power provider would beam energy to it. If someone tried to intercept, your device would notify the power provider.
Sure, it could still be attacked. But it’s not like it’s that hard to wire around an existing power meter, either. Most people are honest and there are big penalties for getting caught.
There are essentially three possible methods for wireless power. You can transmit significant amounts of power, or you can transmit it long distances, or you can transmit it safely, pick any two of the three. Induction charging pads provide significant power safely, but the range is limited to be significantly less than the size of the device. Solar power is very long-distance and relatively safe, but it’s a very small amount. Microwave beams or lasers can carry a lot of power a long distance, but will kill any living thing in the beam.
All of these are doable right now, and we probably won’t ever get all three in the same package.
The most significant investigations of wireless power on a practical level are probably the various SPS (Solar Power Satellite) concepts that have been floated in recent decades. The idea of collecting some huge amount of power using solar arrays miles across and in Clarke orbit, then beaming the power to an earthside receiver, has been seriously considered since at least the 1960s.
Is it possible? Yes. Practical? Yes, for certain values of, allowing for around 75% loss between collection and deliverable electricity. Achievable? Yes, in the trillion-dollar range. Safe? Not on your life, because the power delivery beam is arc-seconds away from being a particle-beam weapon of staggering power. The same would be true for any wireless power transmission system with enough capacity to power even a modest, high efficiency house.
And the one thing our future power systems can’t tolerate and must eliminate is high losses. Don’t look for wireless power much above cell-phone recharging levels over a few inches any time soon.
OTOH, we could use it to power our personal aircars. 
Mr. Cecil Adams reviewed What’s up with “broadcast power”? back in 1990. It was impossible then, and there is no reason to be any more optimistic now on any sort of wide scale implementation.
Isn’t this what Tesla was trying to do?
Yes, but through something far closer to pseudoscience than not.
Pretty much. It even worked, for a given value of “worked”. Tesla coils can be used to transmit power through the “ether”, but it’s also a massively inefficient process.
Tesla was a genius and a visionary. Unfortunately, for all his good ideas, several other of his ideas and theories were just wrong or totally impractical.
You could still make that quite safe by having a failsafe that will cut the beam if anything gets close. Say, have a bunch of low-powered lasers in a circle around the power beam that will shut off the main beam if they’re broken.
The size of the circle is determined by the distance between transmission stations and the speed you expect the living thing might be going.
Detecting a bypassed meter is almost glance-at-it easy. Detecting altered broadcast power metering software would require draconic DRM and a locked-down operating system, and for a lot of classes of power-using items that’s a non-starter. (Android has huge market share, for instance. And the Linux OS underneath it is also ubiquitous, and pretty much impossible to lock down. So your metering firmware would have to start with a proprietary framework and work up from there… which increases per-unit deployment costs. Because the per-copy license of proprietary OSs is always higher than the per-copy license cost of Linux.)
My impression, based on reading quite a bit of material about 15 years ago, is that he was a man of early successful ideas and many late ones that were completely wack.
Did ANY of his ideas or inventions past 1900 prove out, in his lifetime or later? It seems that once he got funding for Wardenclyffe and beamed power, he accomplished nothing further of use. (This may have been because his notion of how transmitted power would work was complete nonsense - using the equipment to “pluck the strings of Earth’s magnetic field” and “harvest” the resulting electricity. He also denied atomic theory.)