One of the primary goals of designing communication systems is to achieve high data rates. Due to limited spectrum, users need to share the common resource, which causes interference with each other. Interference in turn creates a bottleneck on the communication rate. Recently two breakthroughs have been made to relieve this bottleneck. One is using multiple antennas known as multiple input multiple output (MIMO) technology and the other is an interference management technique called interference alignment. While much progress has been made on understanding of each individually, relatively little is known about how to use both techniques together to deal with interference. This thesis presents the progress we have made towards determining the capacity benefits of multiple antennas and interference alignment in different network settings and under various assumptions about the channel state information known at the transmitters. The thesis consists of five main results. First, we characterize the optimal degrees of freedom (DoF) of the K user MIMO Gaussian interference channel with M transmit and N receive antennas for each user when the ratio of the maximum to the minimum of M and N is equal to an integer. Second, we study the N+1 user single input multiple output (SIMO) Gaussian interference channel with one transmit and N receive antennas for each user. We characterize the generalized degrees of freedom (GDoF) of the network, which directly leads to a capacity approximation within a bounded gap which is independent of the signal strength. We also derive outer bounds which identify a strong interference regime where the capacity region is established. Third, we characterize the optimal DoF of two classes of finite state compound wireless networks including the multiple-input single-output (MISO) finite state compound broadcast channel (BC) with arbitrary number of users and antennas at the transmitter and the finite state scalar (single antenna nodes) compound X networks with arbitrary number of users. Fourth, we propose a blind interference alignment scheme through staggered antenna switching, i.e., we seek to align interference without any knowledge of the channel coefficient values at the transmitters. This scheme achieves the optimal DoF of the vector broadcast channel where the transmitter is equipped with M antennas and there are K receivers, each equipped with a reconfigurable antenna capable of switching among M preset modes. Fifth, we go beyond the single hop wireless networks to multihop interference networks and characterize the DoF of the 2-source 2-destination 2-hop interference network formed by concatenation of two 2-user interference channels. The key to this result is a new idea, called aligned interference neutralization, that provides a way to align interference terms over each hop in a manner that allows them to be cancelled over the air at the last hop.