Gemara

(Beraisa): The Mitzvah is to leave Ner Chanukah outside Pesach Beiso (the door of one's house). At a time of danger, it suffices to leave it on one's table.

(Rava): Rav Huna holds that if the Ner extinguished, one must relight it.

(Mishnah): If Reuven's camel, laden with flax, was walking in Reshus ha'Rabim, and caught fire from Shimon's lamp, if the lamp was outside, Shimon is liable for the resulting damage.

R. Yehudah says, if it was Ner Chanukah, he is exempt.

(Ravina): From R. Yehudah, we learn that Neros Chanukah must be placed within 10 Tefachim of the ground.

If not, Shimon would be liable. He should have put it higher than a camel and its rider, to avoid damage!

Rejection: Chachamim did not obligate one to place it so high, lest he refrain from the Mitzvah.

Rishonim

Rambam (Hilchos Chanukah 4:7): The Mitzvah is to leave Ner Chanukah on Pesach Beiso.

Rambam (8): At a time of danger, it suffices to leave it on one's table.

Ran (9b DH v'Im): At a time of danger, when they decreed against Mitzvos, one puts the Ner Chanukah on his table (even though) one who sees thinks that the Ner is not for the Mitzvah, rather, it is his lamp (for his use).

Tosfos (21a DH d'Iy): After (people cease to be in the market), the time has passed. The Ri Pores says that one must be careful to light immediately at night. If he did not, he lights due to Safek, for the Gemara gave other answers. The Ri says that nowadays, there is no concern for when we light.

Or Zaru'a (323) Nowadays that there is no danger, I do not know why people do not light in the Chatzer.

Pesach ha'Dvir (4): I.e. even though there is no danger nowadays, the custom is to light on one's table. Ba'al ha'Itur tried to explain that once the custom arose due to danger, it remained. Surely, if one can light outside, this is the ideal Mitzvah.

Shibolei ha'Leket (185): Since the custom was to light inside at a time of danger, this became the custom.

Ritva (21b DH uv'Sha'as): This is not only if there is mortal danger. Surely, one should not be killed for an Aseh, like we say about Tefilin (49a). Rather, it is danger of pain or animosity, like in France. Therefore, my Rebbi said that when it is windy and one cannot light outside, he lights in the house.

Yisa Yosef (ha'Gaon R. Y. Efrati Shlita OC 1 p.217): The Ritva holds that even before danger, one who lit on his table was Yotzei b'Di'eved. If not, what was his proof? The Gemara did not discuss a time of danger, therefore one is not Yotzei on his table! Rather, we must say that b'Di'eved one fulfills Ner Chanukah [even without danger]. However, if so, what was the enactment for times of danger? Surely one should do so (fulfill the Mitzvah in a b'Di'eved way to avoid danger), since he cannot publicize the miracle, due to danger! It is no Chidush that one need not endanger himself to light outside. One need not be Moser Nefesh for this! What was the Ritva's source that we do not discuss mortal danger? It seems that this is like he wrote in the name of Sefer ha'Terumah, that one may not light after people cease from the market [according to the first answer in the Gemara] only in those days, when they lit outside the opening, and there is no longer a Heker (reminder, i.e. of the Nes) for people of Reshus ha'Rabim. We light indoors, so the Ner is only for the household, so one may light the entire night until dawn. The Ritva said that based on this, we can say that if one did not light, he may light outside until that time, but after this one may light only inside. Also they, (i.e. before the danger) if one could not make a Heker for Reshus ha'Rabim, he was not exempt from making a Heker for himself and his household. He holds, unlike Tosfos, that even according to this answer, b'Di'eved one is Yotzei on his table even before the danger. If so, we cannot say that the enactment was to light on his table at the time of danger, for this is obvious! Rather, the danger is not mortal. Rather, it is danger of not fulfilling the Mitzvah, e.g. pain or animosity. Then it was enacted to light inside. Therefore, one may light inside even due to wind.

Poskim

Shulchan Aruch (OC 671:5): The Mitzvah is to leave Ner Chanukah at the opening next to Reshus ha'Rabim. At a time of danger when he may not fulfill the Mitzvah, it suffices to leave it on his table.

Magen Avraham (5): The Ran says even though at a time of danger one leaves it on his table, and he is forced to benefit from it, still he needs another Ner for a Heker. This is the source for the custom to light a Shamash.

She'alas Ya'avetz (1:149): It is almost a Chiyuv to make a lantern for Ner Chanukah with glass walls, so it will not extinguish in the wind. If one put Ner Chanukah where there is wind, and it extinguished, he must relight it. In the days of the Gemara they lit at Pesach (the opening of) ha'Chatzer outside, like the Mitzvah. It is windy outside. It is unlikely to burn the required time! We must say that they lit in lanterns. Even through a glass, this is considered that one could benefit from the light, like we say about Ner Havdalah. Do not challenge me from R. Yehudah, who exempts (a fire that resulted from) Ner Chanukah. (We do not say that he is liable for not putting it in a lantern to avoid fires.) Rabanan, who obligate, support me!

Note: It seems that Rabanan obligate because he should have put it above 10 Tefachim. According to the Ya'avetz, why did the Gemara discuss only the height, and not a lantern?

She'alas Ya'avetz: Really, even in a lantern, it could get knocked over and cause a fire. It is advisable to light in a lantern. I do not call it a Chiyuv, for I did not see Rabanan do so. This does not mean that they disagree with me. Since we light inside, and there one can avoid extinguishing it, one need not exert himself and spend much money to get such a lantern. If one could get one easily, he should, even when lighting inside! If I can, I will make such a lantern.

Minchas Yitzchak (6:66): The Or Zaru'a connotes that the custom to light inside nowadays is not based on current danger. The Magen Avraham (671:8) says that if one has a window close to Reshus ha'Rabim, he lights there, for this is not dangerous. This connotes that nowadays we light inside due to danger! See Yad Efrayim (who says that the text of the Magen Avraham should say "for nowadays there is no danger.") However, if so, why don't we light at Pesach Beiso, like in the days of the Tur? Nimukei Orach Chayim says that it is windy in winter, and outside it will almost surely extinguish (therefore, we light inside). However, the Poskim did not say that the Mitzvah is to light outside (perhaps this should say inside - PF) due to this. If one needed to light outside in a lantern, the Poskim should have said so! Nimukei Orach Chayim overlooked the Sha'arei Teshuvah.

Sha'arei Teshuvah (673:13): She'alas Ya'avetz holds that it is advisable to light in a lantern even when lighting inside! I did not see anyone do so.

Minchas Yitzchak: She'alas Ya'avetz himself said that he did not see Rabanan do so! However, he said that it is proper to do so if it is not hard. The Sha'arei Teshuvah shows that we do not hold like him, for if we held like him, surely someone would have done the ideal Mitzvah even if it is hard, or someone would have been able to make a lantern easily.

Aruch ha'Shulchan (671:24): Nowadays we do not light outdoors even though there is no danger, for in our lands it is cold and windy in winter, and it is almost impossible to light outside if not in a glass box, and Chachamim did not exert people so much. Also, there would be less Heker of the Mitzvah. Also, they would not let people do so everywhere. Therefore, we all light indoors.

Minchas Yitzchak (ibid.): Aruch ha'Shulchan agrees that when possible, it is better outside. I do not understand why there is less Heker in a lantern. However, I did not see Tzadikim of the generation light outside. Also in Eretz Yisrael only a minority light outside. Imrei No'am (2:29) brings from Megilas Ta'anis that the Mitzvah is to light on Pesach Beiso, but if he fears due to scoffers he lights inside at the Pesach Beiso. At a time of danger, he light on one's table. Tosfos Chadashim says that nowadays there are scoffers.

Halichos Shlomo (Mo'adim 14:16): One who lights in the house on his table is Yotzei b'Di'eved. Also the Steipler (Orchos Rabbeinu 3 p.10) said so. The Gemara says that the Mitzvah (i.e. l'Chatchilah) is at Pesach Beiso. However, the Rambam connotes that it is Me'akev. Nowadays, many light l'Chatchilah in the house. They learn from the Gemara that at a time of danger one light on one's table and "this suffices", i.e. from then the law changed, and one may light on one's table.

Yisa Yosef (p.219): Maharil Diskin says that one must be careful when lighting outside at a time of a strong wind lest the Ner extinguish before he closes the glass box. If one lights in a place where if he does not close the box, it will extinguish, this is like lighting without enough oil to burn the required time. He used to light when the box is closed. He stuck the Shamash in from underneath. Ha'Gaon R. Y.S. Elyashiv Shlita is not concerned for this. He says that in the days of Chazal they used to light in glass boxes, so the Neros will be visible, and they were not concerned lest the Neros extinguish in the short time between lighting and putting the glass to block the wind. Perhaps this is because he could put the glass there immediately, this is not like lighting where they will surely extinguish, like it says in Salmas Chayim.

Igros Moshe (OC 4:105 DH ul'Fi): Even according to the opinion that the Mitzvah was enacted only until people cease from the market, it was not enacted that publicizing the Nes is essential to the Mitzvah. Therefore, at a time of danger, they did not need a special enactment to permit lighting on one's table. The Magen Avraham (672:6) says that publicizing the Nes is essential, so one who comes home when everyone is sleeping must wake someone in order to light with a Berachah. This is astounding. Sha'ar ha'Tziyon (672:17) says that we do not protest against one who blesses without concern for this. I say that one must do so.