In this dissertation, we discuss topics in electroweak symmetry breaking and related phenomena. A quick review of the Standard Model of particle physics is given in Chapter 1. There we also discuss its hierarchy problem and a possible solution-- the Littlest Higgs model. In Chapter 2 and 3, we show that the Littlest Higgs Model and its variants do not successfully solve the hierarchy problem. In Chapter 4 we explore the possibility of spontaneous CP violation in the Littlest Higgs and related models. Another topic that we explore is the existence of a light dilaton, a pseudo-Nambu-Goldstone boson of a spontaneously broken scale symmetry, which is the subject of Chapter 5