The Hebrew word "Satan" means "Hinderer." To hinder someone means to hold him back, to try to prevent him from doing something. G-d created the Hinderer to give us work to do in this world. Satan is here to make things difficult for us, so we can overcome our evil temptations, (Yetzer HaRa) and PASS the test. That is the purpose of Satan. Satan is an angel whose purpose has been determined by G-d. 

Think about it, G-d can do anything. It is said that the only thing that is beyond His power is the fear of Him; that is, we have free will, and He cannot compel us to do His will. This belief in G-d's omnipotence has been sorely tested during the many persecutions of Jews, but we have always maintained that G-d has a reason for allowing these things, even if we in our limited perception and understanding cannot see the reason. 

A machine does not have free will, it can only do what it was designed to do, and a machine cannot love. G-d created us to love him, as he loves us, to love, we must have the will to love, to love from out of free will. One of the ways we show our love is to obey his commandments of which Satan is always tempting us to disobey.

Satan was created by G-d to test our love for G-d. Each of us every day fights with Satan, remember the account of Jacob wrestling with the angel? We all have temptations, throughout the day. But we, as the Children of Israel, have the power to overcome even angels, if we work at it. Therefore, the Talmud says that men are greater than angels, for we can fight with an angel (Satan) and win.
Satan is not, as the Christians think, a rebellious angel. How impossible! The angels are spiritual and holy, without any physical or unholy presence, and the presence of Hashem's holiness permeates them entirely. Angels, unlike humans, are therefore constantly and fully aware of Hashem's Presence everywhere. Could you stay dry in the ocean? An angel could not stop being holy, and can do no wrong. There is holiness everywhere in Creation, everywhere in the universe, and angels are made of the same thing. An angel could not stop serving G-d even if he tried.

Furthermore, humans have Satan to tempt us. Angels have no Satan to tempt them. Who would be Satan's Satan? An ultra-Satan?

The truth is that Satan has a job to do, just like every other angel. And angels have no free will. They do as Hashem commands them.

Humans can improve themselves, and that is their purpose in this world. Angels, however, cannot improve themselves. That's not their purpose. Angels are therefore said to be "standing." They cannot become better, and they cannot rise any higher than they are. They are, so to speak, standing.

Isaiah, when describing a Heavenly scene, says "Seraphim were standing around Him...." (Isaiah 6:2). (Seraphim are a type of angel.) Spiritually, angels are stuck at whatever level Hashem created them.
Humans are different. Humans can rise by improving themselves. For that reason, we are described as "walkers." Therefore the Prophet Zachariah told the High Priest, "This is what Hashem, L-rd of Hosts says: if you walk in My ways, and if you observe My safeguards, you and your sons after you will be the High Priests, and you and your sons will thus guard my Holy Temple, and I will make you walkers among these who are standing" (Zachariah 3:7).

In other words, Hashem was promising the High Priest that he and his children will be High Priests, and also will merit reward in the Afterlife, in the World of Souls, where righteous people go after death.

The Prophet Zachariah was saying that in the Next World they will be walkers among the standers, which means humans among angels.

So the angels are referred to as perpetually standing, but we are movers. Our purpose is to keep on moving, to keep on improving ourselves, and to keep on rising.

And how do we do it? By constant battle with the Evil Inclination.

So now we have to revise our understanding of Satan. Satan is not a fallen angel. Satan is merely an angel with a dirty job. Satan does not have a rival kingdom. Satan is not in competition with G-d, and Satan does not want followers or worshipers. He's not even happy when people obey him and sin.

Satan is the angel who tempts us, and the angel who prosecutes us in Heaven. He is also the Angel of Death. The angel who tries to make us sin is the same angel who accuses us in the Heavenly Court, and the same angel who carries out the death sentence.

So, no, Satan does not wear a red suit, or carry a trident. Nor does he wear a business suit. Satan is a force of evil in the world that we must resist. Satan most often appears as a desire within you. Of course, there is no shortage of things in the world to tempt us to sin.

And Satan has many "helpers," many of whom don't even know they are helping him. A shady-looking character in the street walks over to you and offers to sell you some stolen property, for example. He's not Satan. He's someone who has not resisted Satan, and has decided to do evil. He's now trying to tempt you to sin, but not because he wants you to sin per se. He personally has something to gain from your sinning.

Whenever a human being tries to tempt another person to sin, it's because he himself feels he can gain something from it. It may be simply that he doesn't want to sin alone. Or maybe he needs your help. Or maybe he just gets emotional satisfaction out of seeing you go against what you believe (in which case he is a very sick person, but unfortunately not unusual). There could be any number of motivations.

Likewise, the snake in the Garden of Eden was not Satan either, though confused Christians think it was. He was what the Torah calls a "Seducer," someone who, for whatever reason, tries to get other people to sin.

How does one recognize Satan? For that we need to live a Torah life. This means a host of things that work together. To mention a few: Torah study, spending quality and quantity time among Observant Jewish people, learning from Rabbis and other religiously developed Jewish people, periodic introspection, and actual self-development by means of performing the Mitzvos. It is difficult (if at all possible) to cite any of these as being more important than any of the others.
None of us are capable of destroying Satan. What we are expected and commanded to do is to gain the upper hand over our personal Satans. And Hashem helps us do this, constantly. The Talmud says that the Evil Inclination constantly attempts to destroy us spiritually, and Hashem constantly helps us and gives us the means with which to overcome our Evil Inclinations. 

When this world comes to an end, and the Next World begins, the Day of Judgment will take place. After that, Satan's work will be done. There will no longer be sin, and there will no longer be death. All judgment will have been passed and performed. There will no longer be any need for a Tempting Angel, an Angel of Death, or a Prosecuting Angel. Satan will cease to exist. It will not be a sad day at all.

Nor will it be unfair treatment of Satan. It will be like turning off a machine. Angels are not like humans, with human emotions and desires. They exist merely to follow Hashem's instructions, for the greater glory of Hashem.

That's the reason we exist too -- to follow Hashem's instructions for the greater glory of Hashem. So Satan was created to struggle against us, and we were put into this world to struggle against Satan.

But that was not the purpose of our being created. When the struggle is over we will begin to receive the reward for having struggled. We will be brought in to the Next World, and the struggle will end.

That's when the good times will begin.