This excerpt is taken from Sheikh Hafiz Mubashir Hussain Lahori's book Signs of the Day of Judgment in the Light of Authentic Hadiths.
Sign of the Day of Judgment: Islam will enter every household:
عن المقداد بن الأسود رضى الله عنه يقول : سمعت رسول الله صلى الله عليه وسلم يقول : لا يبقى على ظهر الأرض بيت مدر ولا وبر إلا أدخله الله كلمة الإسلام يعز عزيز أو ذل ذليل إما يعزهم الله عز وجل فيجعلهم من أهلها أو يذلهم فيدينون لها
It is narrated from Hazrat Miqdad bin Aswad (may Allah be pleased with him) that "I heard the noble command of the Messenger of Allah (peace be upon him): There will not remain a house or a tent on the earth in which Allah Almighty will not cause the religion of Islam to enter. With the honor of the honorable (people) or with the disgrace of the disgraced (people), that is, either Allah Almighty will honor those people in such a way that they become among the Muslims, or He will disgrace them so that they become dhimmis and subjugated for this (religion)."
Reference: (Ahmad (5/6) Hakim (476/4) Al-Sunan Al-Kubra (181/9) Al-Tarikh Al-Kabir (151/2) Majma' Al-Zawa'id (8/6)
Hazrat Tamim Dari (may Allah be pleased with him) says that I heard from the Messenger of Allah (peace be upon him): "This religion will reach every place where the cycle of day and night exists. Allah Almighty will cause it to enter every (tent) fragile and solid house with the honor of the honorable and the disgrace of the disgraced. Those who gain honor will become Muslims, while those who gain disgrace will remain disbelievers."
Hazrat Tamim (may Allah be pleased with him) says that I have experienced this in my family; those who became Muslims attained a position of dignity and honor, and those who remained disbelievers were humiliated and forced to pay jizya.
Reference: Ahmad (1441/4) Hakim (477/4) Al-Sunan Al-Kubra (181/9) Al-Tarikh Al-Kabir (150/2) Al-Zawa'id (7/6) Al-Mu'jam Al-Kabir (1280) Al-Silsilah Al-Sahihah (32/1)
Benefits:
The dominance of Islam over the entire earth is a sign of the Day of Judgment, the occurrence of which is inevitable because Allah Almighty has promised His servants:
وَعَدَ اللَّهُ الَّذِينَ آمَنُوا مِنكُمْ وَعَمِلُوا الصَّالِحَاتِ لَيَسْتَخْلِفَنَّهُمْ فِي الْأَرْضِ كَمَا اسْتَخْلَفَ الَّذِينَ مِن قَبْلِهِمْ وَلَيُمَكِّنَنَّ لَهُمْ دِينَهُمُ الَّذِي ارْتَضَىٰ لَهُمْ وَلَيُبَدِّلَنَّهُم مِّن بَعْدِ خَوْفِهِمْ أَمْنًا
"Allah has promised those among you who believe and do righteous deeds that He will surely grant them succession [to authority] upon the earth just as He granted it to those before them and that He will surely establish for them [therein] their religion which He has preferred for them and that He will surely substitute for them, after their fear, security."
Reference: (An-Nur: 55)
This mentioned sign of the Day of Judgment and the divine promise has partially been fulfilled during the era of the Companions and the period of the best of generations. Allah Almighty granted Muslims dominance over the earth, elevated Islam, conquered distant lands such as Egypt, Syria, Rome, Iran, Africa, and Europe. The earth was cleansed of disbelief, polytheism, and tyrannical systems, and the flag of Islamic thought, culture, and civilization was raised throughout the world.
The promise of earthly caliphate was conditional upon faith and righteous deeds. As the condition of faith and righteous deeds among Muslims diminished, the conditional promise (of caliphate) also faded away.
Adhering to Islam is the honor of this world and the hereafter; otherwise, it is destruction and failure.
The second and final part of the promise of caliphate will be fulfilled when Muslims revive the condition of faith and righteous deeds, and this will not be possible before the appearance of Imam Mahdi and Hazrat Isa (Jesus) عليه السلام.
Promise from the Tongue of Prophethood:
The Prophetic hadith is: "As long as Allah wills, prophethood will remain among you, then Allah will take it away. Then the caliphate based on the method of prophethood will be established as long as Allah wills, then Allah will end it and in its place, a devouring monarchy will be established, and it will remain as long as Allah wills. Then by the will of Allah, it will come to an end, and then there will be a period of tyrannical kingship, which will last as long as Allah wills. Then by the will of Allah, it will also come to an end. Then the caliphate based on the prophetic method will be established (again)." Then the Prophet ﷺ remained silent.
Reference: (Ahmad: 273/4)
