Alignment-free (AF) approaches have recently been highlighted as alternatives to methods based on multiple sequence alignment in phylogenetic inference. However, the sensitivity of AF methods to genome-scale evolutionary scenarios is little known. Here, using simulated microbial genome data we systematically assess the sensitivity of nine AF methods to three important evolutionary scenarios: sequence divergence, lateral genetic transfer (LGT) and genome rearrangement. Among these, AF methods are most sensitive to the extent of sequence divergence, less sensitive to low and moderate frequencies of LGT, and most robust against genome rearrangement. We describe the application of AF methods to three well-studied empirical genome datasets, and introduce a new application of the jackknife to assess node support. Our results demonstrate that AF phylogenomics is computationally scalable to multi-genome data and can generate biologically meaningful phylogenies and insights into microbial evolution.