Species tree-aware phylogenetic methods model how gene trees are generated along the species tree by a series of evolutionary events, including the duplication, transfer and loss of genes. Over the past ten years these methods have emerged as a powerful tool for inferring and rooting gene and species trees, inferring ancestral gene repertoires, and studying the processes of gene and genome evolution. However, these methods are complex and can be more difficult to use than traditional phylogenetic approaches. Method development is rapid, and it can be difficult to decide between approaches and interpret results. Here, we review ALE and GeneRax, two popular packages for reconciling gene and species trees, explaining how they work, how results can be interpreted, and providing a tutorial for practical analysis. It was recently suggested that reconciliation-based estimates of duplication and transfer frequencies are unreliable. We evaluate this criticism and find that, provided parameters are estimated from the data rather than being fixed based on prior assumptions, reconciliation-based inferences are in good agreement with the literature, recovering variation in gene duplication and transfer frequencies across lineages consistent with the known biology of studied clades. For example, published datasets support the view that transfers greatly outnumber duplications in most prokaryotic lineages. We conclude by discussing some limitations of current models and prospects for future progress.