Phylogenetic tree inference is a fundamental tool to estimate the ancestor-descendant relationships for different species. Currently, it is of great interest to explore the evolutionary relationships for a set of species for which DNA data have been collected and thus accurate and efficient methods are required to estimate phylogenetic trees. However, because the evolutionary relationships can be analyzed at two distinct levels (gene trees and species trees), and it is not necessary for the gene trees and species trees to agree with one another, phylogenetic inference has become increasingly complicated. Incomplete lineage sorting (ILS) is considered to be one of the major factors that cause disagreement between species trees and gene trees. The coalescent process is a widely-accepted model for ILS, and numerous genealogy-based phylogenetic inference methods have been established based on the coalescent model. In this thesis, coalescent-based methods for phylogenetic tree inference are studied. In Chapter 2, the expected amount of incongruence between gene trees under the same species tree is considered. More specifically, the extent of gene tree incongruence arising from incomplete lineage sorting, as modeled by the coalescent process, is computed. The results in Chapter 2 highlight the fact that substantial discordance among gene trees may occur, even when the number of species is very small. In Chapter 3, a coalescent model for three species that allows gene flow between both pairs of sister populations is proposed, and the resulting gene tree history distribution is derived. The results suggest conditions under which the species tree and associated parameters, such as the ancestral effective population sizes and the rates of gene flow, are not identifiable from the gene tree topology distribution when gene flow is present, but indicate that the coalescent history distribution may identify the species tree and associated parameters. In Chapter 4, a rooting method based on the site pattern probabilities under the coalescent model is developed. The proposed technique provides a method to root every four-taxon species tree within a larger species tree of more than four taxa. The inferred roots for the four-taxon subtrees are then used together to estimate the root for the larger species tree. This rooting method is a computationally feasible method, and is the first method proposed to root a species tree that explicitly incorporates the coalescent process.