AB1GA's advice about antennas and tuners:

You have two kinds of components, sources and loads. Your transmitter is a source, your antenna system is a load.
Sources can be conveniently represented as a voltage in series with a an impedance, called the source impedance.
Loads can be conveniently represented as an impedance only, called the load impedance.
Note that I said impedance, not resistance, which means a resistance in series or parallel with a reactance.

In electrical circuit theory, there's this thing called the Maximum Power Transfer Theorem. It says that when a source is connected to a load, maximum power is transferred to the load when the source and load impedances are complex conjugates of each other, that is, the resistive parts of the impedances are equal, and the reactances are equal in magnitude but of opposite sign. For example, if the source impedance is 50+j300 ohms, the load has to be 50-j300 ohms for maximum power transfer.

Almost all transceivers are designed to drive a load that's 50 ohms, purely resistive.
There are two problems with this:
a. Antenna impedance is dependent on geometry, frequency, ground conditions, and loads of other things.
b. The antenna is far away from the transmitter, and is connected to it by wires. They complicate things.

The wire connecting the two bits is called the feedline. It has a number of interesting features:
a. It has a characteristic impedance which is dependent entirely on its construction, i.e. frequency independent.
b. If the source impedance, load impedance and feedline impedance are all the same, the feedline is electrically invisible.
c. In the case of (b), the peak RF voltage and current are the same all along the line.
d. If the impedance of the antenna isn't the same as that of the feedline, the feedline transforms the impedance of the antenna to another value at its input end; this value depends on the antenna impedance, the feedline impedance, and the length of the feedline in wavelengths, which is dependent on frequency.

So what?
a. Since the antenna impedance varies with frequency, and the transformation of the impedance by the feedline changes with frequency, you can bet your bippy that the impedance at the input to the feedline, where you connect your transmitter, is not 50 ohms purely resistive. No maximum power transfer for you!
b. In those places where the impedance changes, part of the power flowing from the transmitter to the load is reflected back toward the transmitter, where the waveforms add.
c. Now instead of the peak voltage and current being the same along the line, the peak values themselves increase and decrease. The ratio of the highest peak voltage along the line to the lowest peak voltage along the line is called the standing wave ratio, or SWR.
d. In a theoretical system, SWR means nothing, it's just a parameter of a given feedline in a given application.
e. In a real system, high SWR means higher voltages and currents on the feedline. That means greater ohmic losses in the line and the risk of voltage breakdown in the feedline (bad), or in your power transistors (much worse). That's why rigs reduce power at high SWR, to protect themselves from excess voltage or current.

And tuners?
a. A tuner is a circuit designed to transform one impedance to another, just like a transmission line. But it's a lot easier to vary the values of capacitors and inductors than it is to change feedline lengths, at least at HF/VHF.
b. The cleanest tuner solution is one directly at the feedpoint of the antenna. You transform the impedance of the antenna to the impedance of the feedline, which is itself the same as the transmitter output impedance, and all is swell.
c. Problem with (b): since the impedance varies with frequency, you have to adjust the tuner as you change frequency. How do you do that when the antenna is a hundred feet up and the tuner is 99 1/2 feet up. Remote tuner, but that's complicated, and there are simpler, cheaper ways.
d. You accept that your antenna will have a limited frequency range, and put a circuit there (called a matching network) at the antenna that gets you close enough to feedline impedance to avoid arcing and melting. Then, at the transmitter, you use another tuner to tune it the rest of the way. You can use a number of techniques to make the impedance of your antenna less sensitive to frequency, but basically, you only use your antenna at those frequencies where it is safe, as indicated by your SWR meter, and learn to live with your restrictions.

But what about the 135' 80-10 m doublet? How can it work over such a wide frequency range?
a. The magic of the 135' doublet isn't in the antenna, but in the feedline. It's open wire line.
b. Open wire line has very small loss, and the wide spacing of the conductors makes it more resistant to arcing.
c. That means that open wire line is very tolerant of high SWR at amateur power levels.
d. That means you don't fuss with feedpoint matching networks, accept the loss in the feed line, and use just one tuning network at the transmitter to keep your rig happy.