We use the 
word “love” in a variety of ways. One minute we say that love our children; the next minute we say that we love peanut butter. The Greeks were far more nuanced with their words for love.
Agape, the most radical of the loves, is selfless love. Extending love, care, and concern to people regardless of whether the individual was family, friend, or stranger. Some refer to this as God-like love or gift love. The Apostles used a form of agape to describe God’s love for the world (John 3:16), the love between a husband and a wife (Eph. 5:25) as well as the love that should exist between Christians (1 John 3:11).
Philos, friendship love is where we get the name of the city of “Philadelphia” (“city of brotherly love”). Beyond a mere Facebook connection, friends care for one another and show loyalty to one another. A form philos is found in Proverbs 17:17 “A friend loves at all times, and a brother is born for adversity” (LXX). Jesus called Lazarus his philos (John 11:11).
The idea of family is bound with the third love, storge. Storge describes the bond and affection that comes in the context of family, such as the love among siblings. Forms of storge are rare in the Bible, though not absent. In 2 Timothy 3:3, Paul uses the “a” to negate stroge when he writes about the last days: “People will be lovers of themselves, lovers of money, boastful, proud… without love [astorgoi].” The KJV translates astorgoi “without natural affection.”
Through the power of the gospel, Christians are to display these three loves to one another. I know of no other passage in Scripture that employs a form of these three loves in such close proximity as Paul does in Romans 12:9-10
“Love [agape] must be sincere. Hate what is evil; cling to what is good. 10 Be devoted [philostorgoi] to one another in brotherly love [Philadelphia]. Honor one another above yourselves.” Romans 12:9-10
Listen to the sermon here.