Rashi: It was to drive Madai.

Radak: Madai and Paras first went to the north to destroy Bavel; afterwards, they ruled over all kingdoms of the world.

Malbim: This is Romi. It went to the north to seize kingship there. Also it will be northern - from there the evil will come to destroy Yerushalayim.

Rashi: It is to drive Paras. Paras and Madai are in the north, and they ruled over Bavel.

Radak: This is Malchus Yavan, which was after Paras and Madai. It overpowered; Alexander Mukdan, their first king, killed Daryavesh in Bavel and took kingship from him. He and those after him ruled over the entire world.

Malbim: They did not go in a particular direction. They will spread in the east and west. These are all the kings who ruled after Romi's kingdom ceased.

Rashi: It is to drive [Alexander] Mukdan. He will take kingship from Paras. Radak - Rav Sadya Gaon on Daniel said that Melech Mukdan is "Melech ha'Negev" (Daniel 11:5).

Radak: Teiman is the south. Romi is to the north, and Luli'anus Keisar, who ruled over Romi, began to fight Yavan, and the beginning of his wars went to Egypt in the south. Yavan was ruling in the entire world, and Luli'anus Keisar overpowered them. He transferred the kingship from Yavan to the Romiyim.

Malbim: Close to the time of Mashi'ach will be a spotted kingdom from the whites, just there will be also black and white spots. They will be aroused to war. Gog and Magog will come from them, from Yarkesei Tzafon, to Teiman (the south) - Eretz Yisrael. They will divide into two camps, which will fight each other, like I explained in Yechezkel Perakim 38-39. Bnei Edom will be aroused to conquer Eretz Yisrael from the Yishmaelim (the Amatzim); they will Mis'ametz (invigorate themselves) to oppose those who fight them.

Rashi: They were for Bavel. Bavel already ceased.

Malbim: The first verse already explained them (1:8-10).