Electronic states that could propagate long distances without power dissipation and with spin coherence (i.e. without losing information about their spin state) would be desirable for the design of energy efficient electronic devices and to make reality theoretical proposals of quantum computation devices. Topological insulators are recently discovered materials that may potentially offer these foreseeable properties. These materials are insulating in bulk, but present metallic edge states that are naturally preserved from backscattering by time reversal symmetry. In other words, the propagation direction and the spin state are correlated in these systems, so in order to be scattered, electrons must flip their spin (break time reversal symmetry). Experimental results already indicate the existence of such states but still a huge experimental effort is necessary to reach the necessary understanding and the technical skills to take advantage of the predicted surprising properties of these materials. Specially promising are the expected consequences of the application of a local magnetic field to these topologically protected states. Between other consequences, this would allow the confinement and manipulation of these states and would be therefore a first step towards the fabrication of theoretically proposed devices based in the special properties of these materials. We propose here a comprehensive study of the effect of magnetic field in different topological systems (HgTe quantum wells and the so called 3D topological insulators) by means of state of the art nanofabrication and characterization techniques, including an innovative combination of scanning probe microscopies and electronic transport measurements. Our aim is to provide a complete (local and non-local) picture of the electronic transport and electronic structure characteristics of these materials as well as to provide means to manipulate and confine their exotic topological states.