We review magnetic monopoles and dyons of one-half topological charge with finite energy in the SU(2) Yang-Mills-Higgs theory. The half-monopole can exist individually, where it is located at the origin of the coordinate axes r = 0. It can also coexist with a ‘t Hooft-Polyakov monopole, with the one-monopole with charge +1 at the positive z-axis and a half-monopole with charge – ½ at the origin. Both of these axially symmetric configurations possess finite total energy and magnetic dipole moment. The total energy is found to increase with the strength of the Higgs field self-coupling constant λ. The magnetic dipole moment and the dipole separation (one plus half-monopole) decrease with λ. Both the two configurations are non-BPS solutions even in the BPS limit when the Higgs self-coupling constant vanishes. By switching on the time component of the Yang-Mills potential, electric charge is introduced into the system, where we now have half-dyon and one plus half-dyon. Besides possessing electric charge which varies with λ and electric charge parameter η, the configurations also exhibit critical behaviour in total energy, electric charge, and dipole moment, when η→1.