Fine-scale evolutionary dynamics can be challenging to tease out when focused on the broad brush strokes of whole populations over long time spans. We propose a suite of diagnostic analysis techniques that operate on lineages and phylogenies in digital evolution experiments, with the aim of improving our capacity to quantitatively explore the nuances of evolutionary histories in digital evolution experiments. We present three types of lineage measurements: lineage length, mutation accumulation, and phenotypic volatility. Additionally, we suggest the adoption of four phylogeny measurements from biology: phylogenetic richness, phylogenetic divergence, phylogenetic regularity, and depth of the most-recent common ancestor. In addition to quantitative metrics, we also discuss several existing data visualizations that are useful for understanding lineages and phylogenies: state sequence visualizations, fitness landscape overlays, phylogenetic trees, and Muller plots. We examine the behavior of these metrics (with the aid of data visualizations) in two well-studied computational contexts: (1) a set of two-dimensional, real-valued optimization problems under a range of mutation rates and selection strengths, and (2) a set of qualitatively different environments in the Avida digital evolution platform. These results confirm our intuition about how these metrics respond to various evolutionary conditions and indicate their broad value.