The great success of comparative methods has been, I think, in testing hypotheses about adaptation. A variety of methods can be applied to test for evolutionary relationships between form and the environment – and, increasingly, organismal function. These methods applied to real data have shed great light onto the myriad ways that species can adapt. This has been a great boon to organismal biology, and comparative methods are now routinely used to analyze and test hypotheses of adaptation across the tree of life. Methods for detecting adaptation using comparative approaches are growing increasingly sophisticated in terms of the types of data that they can handle, including massively multivariate gene expression data, function-valued trait data, and data from genome sequencing. One can only expect this trend to continue.
One thing seems certain after a few decades of comparative analysis: the tempo of evolution is incredibly variable. Rates of evolution vary both through time and across clades, with the quickest rates of both trait evolution and speciation thousands of times faster than the slowest rates. We can see this variation in analyses from relatively simple tree balance tests to sophisticated Bayesian analyses. So, evolution does not tick along like a clock; instead, rates of evolution depend strongly on lineage, time, and place. The details of these relationships, though, remain to be deciphered.
Comparative methods have played a critical role in our understanding of speciation. Studies using lineage-through-time plots have greatly enhanced our knowledge of diversification rates, and a wide range of results have shown increasing evidence for diversity-dependence in speciation (though this interpretation is not without controversy!). This set of studies provide a nice complement to paleobiological studies of diversification rates using the fossil record.
We can already gain some new biological insights as comparisons among clades start to hint at which factors are responsible for the fact that some species are so much more diverse than others. Perhaps for psychological reasons, most studies have tried to determine explanations for the fastest rates of speciation, as seen in young diverse clades like African cichlids and Andean plants. However, given the high potential for speciation and splitting to accumulate species in a geographic landscape, it might be true that the depauperate clades are really the mysterious parts of the tree of life. Many current research programs are aimed directly at explaining differences in diversity across both narrow and broad phylogenetic scales.
Overall, I think it is easy to see why comparative methods have risen to their current prominence in evolutionary biology. Phylogenetic trees provide a natural way to test evolutionary hypotheses over relatively long time scales without requiring any direct historical information. They have been applied across the tree of life to help scientists understand how species adapt and multiply over long time scales.