This document contains notes from a presentation on inferring phylogenetic trees and lateral gene transfer. It discusses challenges with accurately reconstructing the tree of life due to early ancestral signal being lost, biases in models, and lateral gene transfer. Methods for detecting lateral gene transfer like using k-mers or codon usage and phylogenetic discordance are presented. The document also discusses hypotheses for lateral gene transfer involving gene complexity, selfish operons, and public goods. Examples of lateral gene transfer studies in bacteria are provided.