Perturbations in magnetically or electrically ordered materials can form stable defectsthat cannot be erased by local fluctuations. An example is a domain wall between twoareas with differently oriented magnetisation. To remove that domain wall, one wouldhave to switch an extensive region of spins. This would require a large amount of energyand therefore grants the domain wall a certain stability. A tool to generally characterisethe stability of such perturbations is the concept of topology. Topology regulates theallowed deformations that can be applied to an object, thus, it can determine the robustnessof magnetic or electric defects towards external forces. Topology cannot onlyspecify the stability of defects, but can also classify them and reveal unexpected propertiesat such structures. At present, we are only beginning to explore the wide varietyof structures and properties of these topological defects. Developing a fundamentalunderstanding of their physical properties is, however, crucial before utilizing them indevice applications to achieve higher storage capacities and faster processing of information.Therefore, integrating these structures into future nano-electronics requiresfurther investigations into possible defect patterns as well as their properties.The aim of this thesis is to analyse and characterise topological defects in two complementarymodel systems covering defects of both magnetic and electric nature. Scanningprobe microscopy measurements over a wide range of temperature performed onthese materials show the properties of these defects as well as their impact on thesurrounding bulk material. In particular, the work reveals so far unreported topologicaldefect structures and their intriguing properties.By using a magnetic scanning probe microscopy mode, we present the experimentalobservation of different magnetic line-defects with non-trivial topology in the helimagneticphase of FeGe. These line defects include ±pi disclination, edge dislocation andspiral structures. We show that the motion of isolated edge dislocations govern thelocal magnetisation dynamics. Moreover, defects can form chains and build topologicaldomain walls, which are distinctly different from classical antiferro- and ferromagnets.Experimentally, three main types of domain walls are found depending on the anglebetween neighbouring domain orientations. Similar to the magnetic skyrmions thatform in the same material the line defects and domain walls can carry a finite topologicalwinding number. This topological winding number prevents them from non-continuousdeformations, which has a strong influence on the transformation of the helimagneticphase. Thus, going beyond skyrmions, chiral magnets reveal a zoo of magnetic nanoobjectswith non-trivial topology that have a profound impact on the helimagnetic phaseinfluencing the order and mobility of the spin system.In order to study topological defects of electrical nature, we choose naturally occurringcharged ferroelectric domain walls in geometrically driven ferroelectric Er1−xCaxMnO3.These domain walls are two-dimensional topological defect structures. By measuringthe local electronic conductance and electrostatics we demonstrate intrinsic semiconductingtransport properties at charged domain walls. At low temperatures uncompensatedcharges arise, due to a temperature dependent increase in polarisation. Thetemperature dependent occurrence of an electrostatic signal at the domain walls reflectstheir complex screening mechanism, which differs between oppositely chargeddomain walls. This observation of incomplete screening reveals a unique robustness,and therefore their topological properties, of charged domain walls in improper ferroelectrics.The research results of this thesis, thus, provide new insights into complex topologicaldefect structures in magnetic and polar materials using advanced scanning probemicroscopy techniques. They yield fundamental and tech-relevant information, whichcould bring new and complex magnetic and electronic structures into the realm of nanoelectronics.