The emphasis on the Gospel of Luke is, interestingly, the inclusion of Gentiles and all peoples in the ministry and outreach of Christianity and the mission of Jesus. For our world today, I think this has obvious relevance given the way that globalisation has made our world a "global village" and has also increased movement of peoples between countries. Refugees and economic migrants abound in Western countries, and the Gospel of Luke gives us an important message of how we should treat the "alien" in our midst.
One focus of the Gospel of Luke (as with the other gospels in the New Testament) is the life of Jesus. Though much seems the same between this book and the other accounts of Christ's life, the Gospel of Luke has the greatest variety of parables, teachings, and events. As a result, there is much that could be looked at and compared to "our current society."
One easy story that sticks out to me, however, is the story of the Good Samaritan (at the end of Chapter 10). A man is robbed and left for dead on the side of the road. A Priest and a Levite both see him and do nothing. These were examples of "men of God," or at the very least, God's representatives in their day, and they both leave the man for dead. Then a Samaritan passes by, bandages the man's wounds, gives him a ride to the nearest inn, pays for a room, and leaves him with enough money to recuperate. He does all of this, for the most part, anonymously. Ironically, the audience for this very story would have expected the religious men to help. The Samaritan, on the other hand, was considered by the Jews to be ethically and religiously impure. He would have been the last person on their minds who would come along and actually provide help.
The same rings true today. How often have the so-called "religious leaders" failed to provide care for those who need it the most. On the other hand, we frequently read and hear about stories of modern-day "Good Samaritans." Sometimes it is the people society least expects to help who seems to display the most care. Even more, how often do we hear about "Good Samaritan" acts in which the giver remains anonymous?