One that I've not seen gone into depth here is electromagnetic fields, as distinct from "radio".
Marine animals from clams on up either inadvertently or deliberately produce electric signals, and those signals are detected through the water by marine predators (sharks, skates, rays, reedfish, sturgeon, etc). Most have their electroreceptors in ampullae of Lorenzini, and those of sharks are sensitive to 5 nV/cm.
To work at reasonable range, this requires water or conductive ground, however; air is a reasonably good electrical insulator, so I suspect such communication over air would be necessarily short-range.
We can calculate the range and data rate we'd get by comparing to an electric eel.
To emit electricity, electric eels use electroplaques which, arranged in series, emit 860V at 1A and 25Hz.
A shark can detect 1/172,000,000,000th of that voltage over 1cm. So if we can find the sphere that has 172 billion cm surface area, that's the max theoretical distance they could communicate, assuming perfect conductance. That's a 1170m radius (nearly 3/4 mile), so that'd be the max communication range with biological organs that exist on earth.
On a flat plane (eg wet ground), the distance would massively increase because now it's just a disc, not a sphere, to a shade under 274km.
Be warned that this is assuming perfect conduction, not taking into account resistance, impedance, interference, noise, and other confounding effects, all of which would severely decrease this range. akin to saying "The blue whale can emit at 188dB, and the most sensitive hearing of any animal is (I don't know, and have no idea why this is so hard to google) dB, therefore using speech we could communicate out to thousands of miles if we assume air transmits sound perfectly".
It's also assuming that it's OK to electrocute the person next to you in order to shout across to the next room.
At 25Hz, you can transmit a signal of at most 25 bits per second, which is still plenty for speech, with human speech having a bit rate of some 39 bits per second. Cranking it up to 40Hz to get the same rate as speech doesn't seem infeasible, or even higher, plus you can use other modulation schemes to get higher data rates at the cost of range.
Detection of magnetic fields (magnetoreception) has been shown in everything from bacteria on up. Many such animals have been shown to navigate by magnetic fields, for example. But for the most part, we only have hypotheses about how this is done, and don't even know the sensitivity-levels of the sensors.
The study of this area is magnetobiology, and as that page admits in its lede:
Biological effects of weak low frequency magnetic fields, less than about 0.1
millitesla (or 1 Gauss) and 100 Hz correspondingly, constitutes a physics problem.
The effects look paradoxical, for the energy quantum of these electromagnetic
fields is by many orders of value less than the energy scale of an elementary
chemical act. On the other hand, the field intensity is not enough to
cause any appreciable heating of biological tissues or irritate nerves
by the induced electric currents.
That is to say, we not only don't know how animals detect this (though there are plenty of hypotheses), but we don't even have a clue how it's physically possible for them to do it as well as they do.
The page also makes the (unsupported) claim:
Their perception can be on the order of tens of nanoteslas.
So if you want more magic-and-woo SciFi, magnetic stuff is good. If you want Hard Science, maybe best to stick to electric stuff. But remember that they're both just two sides of the same coin! An electric field creates a magnetic one, and vice versa.