Phylogenies are increasingly being used as a basis to provide insight into macroevolutionary history. Here, we use simulation experiments and empirical analyses to evaluate methods that use phylogenies as a basis to make estimates of divergence times and rates of diversification. This is the first study to present a comprehensive assessment of the key variables that underpin analyses in this field – including substitution rates, speciation rates, and extinction, plus character sampling and taxon sampling. We show that in unrealistically simplistic cases (where substitution rates and speciation rates are constant, and where there is no extinction), increased character and taxon sampling lead to more accurate and precise parameter estimates. By contrast, in more complex but realistic cases (where substitution rates, speciation rates, and extinction rates vary), gains in accuracy and precision from increased character and taxon sampling are far more limited. The lack of accuracy and precision even occurs when using methods that are designed to account for more complex cases, such as relaxed clocks, fossil calibrations, and models that allow speciation rates and extinction rates to vary. The problem also persists when analysing genomic scale datasets. These results suggest two interrelated problems that occur when the processes that generated the data are more complex. First, methodological assumptions are more likely to be violated. Second, limitations in the information content of the data become more important.