I am currently reading the autobiography of the Dalai Lama. He writes:

Thus I am believed also to be a manifestation of Chenrezig. In fact, the seventy-fourth in a lineage which can be traced back to a Braman boy who lived at the time of Buddha Shakyamuni. I am often asked whether I truly believe this. The answer is not simple to give, but as a 56-year-old, when I consider my experiences during this present life and given my Buddhist beliefs, I have no difficulty in accepting that I am spiritually connected both to the thirteen previous Dalai Lamas, to Chenrezig and to the Buddha himself.

I think this is very subtle and appealing. Note the emphasis I put on the words: “spiritually connected.” We are not asked to believe a physical rebirth, but clearly our thoughts, our emotions do connect us with the past and the future. Through his upbringing and rigorous and careful education, obviously the present Dalai Lama is spiritually connected to his predecessors.