Status of embryos
הָאִשָּׁה שֶׁהִיא מַקְשָׁה לֵילֵד, מְחַתְּכִין אֶת הַוָּלָד בְּמֵעֶיהָ וּמוֹצִיאִין אוֹתוֹ אֵבָרִים אֵבָרִים, מִפְּנֵי שֶׁחַיֶּיהָ קוֹדְמִין לְחַיָּיו. יָצָא רֻבּוֹ, אֵין נוֹגְעִין בּוֹ, שֶׁאֵין דּוֹחִין נֶפֶשׁ מִפְּנֵי נָפֶשׁ:
If a woman is having trouble giving birth, they cut up the child in her womb and brings it forth limb by limb, because her life comes before the life of [the child]. But if the greater part has come out, one may not touch it, for one may not set aside one person's life for that of another.

מַתְנִי׳ עוּבָּרָה שֶׁהֵרִיחָה — מַאֲכִילִין אוֹתָהּ עַד שֶׁתָּשִׁיב נַפְשָׁהּ.

a pregnant woman who smelled food and had a craving to eat, one feeds her until she recovers, as failure to do so could lead to a life-threatening situation.

רמב״ן תורת האדם שער המיחוש

ואף על גב דתנן (אהלות פ"ז) האשה המקשה לילד מביאין סכין ומחתכין אותו אבר אבר, דאלמא מעיקרא לית ביה משום הצלת נפשות... אפילו הכי לענין שמירת מצות מחללין עליה: אמרה תורה חלל עליו שבת אחת שמא ישמור שבתות הרבה.

Ramban: Torah Haadam

Even though we learned in the mishna in Ohalot that if the woman is struggling in childbirth we bring a knife and cut the fetus limb by limb, so we see that it doesn't have any status that we need to save it... however with regard to it being able to keep mitzvot we break shabbat to save it: The Torah says we should break one shabbat as perhaps he will then keep many future shabbatot.

מַאי טַעְמֵיהּ דְּרַבִּי יִשְׁמָעֵאל? דִּכְתִיב: ״שֹׁפֵךְ דַּם הָאָדָם בָּאָדָם דָּמוֹ יִשָּׁפֵךְ״. אֵיזֶהוּ אָדָם שֶׁהוּא בָּאָדָם? הֱוֵי אוֹמֵר: זֶה עוּבָּר שֶׁבִּמְעֵי אִמּוֹ.

What is the reason for the opinion of Rabbi Yishmael? It is derived from that which is written: “One who sheds the blood of a person, by a person [ba’adam] his blood shall be shed”. The word ba’adam literally means: In a person, and is interpreted homiletically: What is a person that is in a person? You must say: This is a fetus that is in its mother’s womb.

(ב) לפיכך העוברת שהיא מקשה לילד מותר לחתוך העובר במעיה... שהוא כרודף אחריה להרגה ואם הוציא ראשו אין נוגעין בו שאין דוחין נפש מפני נפש וזהו טבעו של עולם:

Therefore a pregnant woman who is struggling in labour, it is permissible to cut the fetus inside her...since it is like someone pursuing after her to kill her. And if the head has come out one may not touch it, as we do not push aside a life for another life, and this is the natural way of the world.

מַכֵּ֥ה אִ֛ישׁ וָמֵ֖ת מ֥וֹת יוּמָֽת׃
One who fatally strikes another party shall be put to death.

למה נאמר איש שיכול אפלו הכה את הנפלים ובן שמונה יהא חייב ת"ל איש מה איש מיוחד שהוא בן קיימה יצאו הנפלים ובן שמונה שאינן בני קיימה:

Why does it say "ish"? Because we might have thought if he hit a fetus or embryo of 8 months gestation he will also be liable, so it comes to teach us "ish" - that just as a man is unique because he is in existence, fetuses are excluded because they are not yet in existence.

מַתְנִי׳ הָאִשָּׁה שֶׁיָּצְאָה לֵיהָרֵג, אֵין מַמְתִּינִין לָהּ עַד שֶׁתֵּלֵד. הָאִשָּׁה שֶׁיָּשְׁבָה עַל הַמַּשְׁבֵּר, מַמְתִּינִין לָהּ עַד שֶׁתֵּלֵד.

In the case of a pregnant woman who is taken by the court to be executed, the court does not wait to execute her until she gives birth. But with regard to a woman taken to be executed who sat on the travailing chair in the throes of labor, the court waits to execute her until she gives birth.

אֵיתִיבֵיהּ רַב חִסְדָּא לְרַב הוּנָא: יָצָא רֹאשׁוֹ – אֵין נוֹגְעִין בּוֹ, לְפִי שֶׁאֵין דּוֹחִין נֶפֶשׁ מִפְּנֵי נֶפֶשׁ. וְאַמַּאי? רוֹדֵף הוּא! שָׁאנֵי הָתָם, דְּמִשְּׁמַיָּא קָא רָדְפִי לַהּ.

Rav Ḥisda raised an objection to Rav Huna. But once his head has emerged, he may not be harmed in order to save the mother, because one life may not be pushed aside to save another life. If one is permitted to save the pursued by killing the minor who is pursuing him, why is this so? The fetus is a pursuer who is endangering his mother’s life. The Gemara answers: it is different there, with regard to the woman giving birth, since she is being pursued by Heaven. Since the fetus is not acting of his own volition and endangering his mother of his own will, his life may not be taken in order to save his mother.

הוֹרוּ חֲכָמִים שֶׁהָעֻבָּרָה שֶׁהִיא מַקְשָׁה לֵילֵד מֻתָּר לַחְתֹּךְ הָעֵבָּר בְּמֵעֶיהָ בֵּין בְּסַם בֵּין בְּיָד מִפְּנֵי שֶׁהוּא כְּרוֹדֵף אַחֲרֶיהָ לְהָרְגָהּ. וְאִם מִשֶּׁהוֹצִיא רֹאשׁוֹ אֵין נוֹגְעִין בּוֹ שֶׁאֵין דּוֹחִין נֶפֶשׁ מִפְּנֵי נֶפֶשׁ וְזֶהוּ טִבְעוֹ שֶׁל עוֹלָם:

Sages ruled that when complications arise and a pregnant woman cannot give birth, it is permitted to abort the fetus in her womb, whether with a knife or with drugs. For the fetus is considered a rodef of its mother. If the head of the fetus emerges, it should not be touched, because one life should not be sacrificed for another, and this is the nature of the world.