Historically, the design of antenna systems has evolved separately from Shannon theory. Shannon theory adopts a probabilistic approach in the design of communication systems, while antenna design approaches have relied on deterministic Maxwell theory only. This thesis introduces a new approach to the design of broadband antennas/arrays based on information theoretic metrics. The thesis is composed of two parts, where in the first part we will study antennas in the context of the the single-input single-output (SISO) wireless systems. In the second part, the extension is made to study multiple-input multiple-output (MIMO) wireless systems, as well as provide some guidelines for practical implementation. In the SISO setting, to obtain the information-theoretic performance limit, and using ideas from Chu and Bode/Fano theories, I characterize the maximum achievable rate over the SISO wireless communication channels under a restriction on the antenna size at the receiver. I first describe an equivalent Chu's antenna circuit under the physical realizability conditions of its reflection coefficient. The physical realizability conditions are then used to determine the shape of the information-theoretically optimal broadband matching network. I also examine the achievable rate in presence of interference showing that the size constraint is immaterial in interference-limited scenarios. By incorporating the finite antenna size constraint using Chu's theory and under the assumption of canonical-minimum scattering (CMS), I derive the MC between two radiating volumes of fixed sizes. In the MIMO setting, with a simple mathematical extension to account for MC (similar to NFC), I present a model for connected antenna arrays with a large number of tightly integrated antennas in a compact space within the context of masive MIMO communication. The system is refereed to as tightly-coupled massive MIMO. The development shows that tight MC widens the operational bandwidth of antenna arrays thereby unleashing a missing MIMO gain that was coined ``bandwidth gain''. For practical implementation of MIMO arrays, I demonstrate a capacity-based design of tightly-coupled connected array \cite{cavallo2011connected} of slot as well as dipole antennas, which is in line with the developed theory as mutual coupling (MC) is known to widen the operational bandwidth of antenna systems.