The Standard Model of particle physics is the best existing theory for describing the interactions between elementary particles. Even though the Standard Model has been confirmed in many experiments, there remain unanswered questions. One of the main questions is how fermions and most gauge bosons get masses; the Standard Model begins with them as massless. The Higgs effect is a mechanism to explain how fermions and several gauge bosons do get masses in the Standard Model. The corresponding Higgs boson is the only particle that has not yet been detected. This Thesis gives a complete review of the Higgs effect and Higgs related topics. It starts with theoretical basics and develops the theory of the Higgs effect within the electroweak section of the Standard Model. The discussion then considers the topics of radiative corrections and the effect of the Higgs boson as a virtual particle, concentrating on the example of the rho-parameter. In addition, experimental and theoretical constraints for the Higgs mass M_H will be given with special emphasis on the Hierarchy Problem which leads to a physically unacceptable Higgs mass when using high energies (of the Grand Unification scale) as a cutoff for the radiative corrections. Furthermore experimental attempts to detect the Higgs boson at LEP2, TEVATRON and LHC will be described and the different decay channels discussed. Finally, alternative theoretical models beyond the Standard Model are motivated and presented, such as supersymmetry, a vectorlike Standard Model and a possible relation between the Higgs and the Inflaton of Cosmology.