Straight Wings VS Delta Wings, Variable wing with Forward swept capability
At low speed, the key to reducing "induced drag" is to have a high aspect ratio, that is, you want wings that are long and skinny. Think gliders. Now of course, these are not easy to build, and for entirely practical reasons you might want something that's more square-ish than a glider. That's one of the many engineering trade-offs every aircraft design requires. Check out the svelt wings on this Q400:



Things become more interesting as speed increases.

First, as you enter the transonic area above around 450 mph, a new form of drag begins to form, the so-called "wave drag". The way to reduce this is to make the wing as thin as possible, or to be more specific, have as little curvature on the top and bottom edge. Ultimately you want an almost flat plate.

Now of course, lift is generated by that curvature, so that's a problem. And when you try to reduce that curvature to lower wave drag but still want the same lift, well then you have to make the wing larger front-to-back (think about it) and now your induced drag goes up, and skin friction too in most cases.

So then there's a trick. If you sweep the wing to the rear then the air flowing over it travels across a longer distance. So it thinks the wing is longer front-to-back and has less curvature, and that lowers wave drag. Yet at low speeds, the air smoothly flows over the curves and sees the original wing profile. So you get a thick wing that looks thin. Check out this F-86, notice that the wings are actually pretty thick:



Now as you go supersonic, things change yet again. In this case the drag is minimized by having the least width you can get away with. So for these sorts of designs you want short stubby wings with lots of chord (front-back) and you end up with the F-104.:



Now you have a wing that is absolutely terrible at low speeds, and for that reason, lots of F-104s crashed while the pilots tried to keep up with the plane while landing at redonkulous speeds needed to keep the thing in the air.

Deltas are mostly just swept wings with the inside filled in. If you want to see an example that really illustrates this, look at the English Electric Lightning:



If they filled in that little part, it would be a delta. But there is one trick that you get in a delta you don't get in a swept wing...

At very high angles of attack, with the nose high, the air along the leading edge of the wing can generate a vortex right along the fuselage. If there is a wing under it, this generates lift. Poorly, with lots of drag, but lift. So then you get this little one-trick-pony effect; this will works really well at high speed, but also works OK at really low speeds too. But it only works if the vortex is above actual wing, so the Lightning didn't get all the advantage here.

The problem with deltas are that they are big and heavy, but they also get more room inside for fuel. More trade offs. But then someone came up with a new idea: make a normal swept wing and then add a little bit of delta:



You can even see the vortexes in this image. In this case the little-bit-of-delta is called a "leading edge extension".

Variable wings are simply an attempt to put all of these on a single aircraft. Rotate them forward and you have a nice long skinny wing like the Q400. Rotate them back and you have a really swept wing or even a delta, and at the same time the width is being reduced. So now you can go fast or slow. Just weighs a lot.

Swept forward is basically identical to swept back. This isn't about lift in this case but an attempt to control something called spanwise flow. Check out this MiG-17's wing:



Do you see those metal plates? What happens on a swept wing is that the shape causes some of the air to move sideways. This is a Bad Thing. So these plates grab sideways moving air and redirect it over the wing again. The same thing happens on deltas, check out the notch on the CF-105, same idea:



Now the idea here is that the wind is following the wing's leading edge. So what happens if you sweep it the other way? Well then it follows the wing into the fuselage, and stops. Presto, problem solved and no plates or notches! The problem is that it's really hard to actually make one that doesn't snap apart, which is why it's not common.