Phylogenies that are reconstructed without fossil material often contain approximate dates for lineage splitting. For example, particular nodes on molecular phylogenies may be dated by known geographic events that caused lineages to split, thereby calibrating a molecular clock that is used to date other nodes. On the one hand, such phylogenies contain no information about lineages that have become extinct. On the other hand, they do provide a potentially useful testing ground for ideas about evolutionary processes. Here we first ask what such reconstructed phylogenies should be expected to look like under a birth-death process in which the birth and death parameters of lineages remain constant through time. We show that it is possible to estimate both the birth and death rates of lineages from the reconstructed phylogenies, even though they contain no explicit information about extinct lineages. We also show how such phylogenies can reveal mass extinctions and how their characteristic footprint can be distinguished from similar ones produced by density-dependent cladogenesis.