One paper I particularly enjoyed was Gary Manning on the use the Elijah and Elisha stories in Luke / Acts. Since my dissertation is on intertextuality or allusions (or whatever we are going to call it these days) this paper was quite stimulating since Manning was working with similar methods although with different texts. He amassed quite a bit of data which supported he contention that Luke conscious patterned stories in Luke and Acts after the pattern of 1 Kings. Manning had linguistic evidence as well as thematic coherence for each of his examples and it was hard to deny that the examples he chose were in fact allusions.
As for why Luke would turn to these sorts of texts. Usually scholars would point out that John the Baptist is like Elijah, so these allusions are natural. But that doesn’t always work since sometimes an allusion describes an activity of Jesus with an allusion to Elijah, or an action of Paul with that of Elisha. Manning suggested that these allusions are less about the man, and ore about the age. Jesus, Peter, Philip, and Paul are all people who are specially endowed with the Holy Spirit just as Elijah and Elisha were. For Luke, the present age is like the days of Elijah in in that the leadership is directed powerfully by the Spirit of God. The new age of the Spirit is like the days of Elijah in many ways, so the allusions are made to highlight the work of the Spirit.
I might suggest another reason for the allusions to the Elijah stories Manning did not include. Jesus describes the present generation as a “wicked and adulterous generation,” one that seeks a sign. The time of Elijah’s ministry was to a similar wicked and (spiritually) adulterous generation, on that sought a sign from God (Mount Carmel) yet did not believe the sign when it was given. Perhaps Luke is drawing our attention to the similarities between Jesus’ audience and the generation of Elijah. If so, I cannot imagine a more stinging criticism of the Pharisees that to imply that they are as wicked as the Israelites at the time of Ahab!