In the last century, the role of magnetic materials has changed drastically. Of all the electronic properties of solids, magnetism maybe became of interest to the widest range of scientists and technologists. In addition to fundamental interests in magnetic properties there is a large and growing technology based interest of the properties of magnetic materials. Quite small improvements in permeability, coercivity or saturation magnetisation can be of great economic significance. On the other hand, the magnetic properties of antiferromagnetic materials were not of technological interest until 1956 where Meiklejohn and Bean reported: “A new type of magnetic anisotropy has been discovered which is best described as an exchange anisotropy. This anisotropy is the result of an interaction between an antiferromagnetic material and a ferromagnetic material”. Meiklejohn and Beans discovery was initiated by the observation that the hysteresis loop of a sample of nominal cobalt nanoparticles was shifted along the field axis after cooling in an applied field. It was subsequently established that the particles had been partially oxidised to CoO which is an antiferromagnet. A biased magnetisation direction in a ferromagnet (FM) provided by an antiferromagnet (AFM), the so-called exchange bias (EB) effect, is nowadays essential to state-of-the-art magnetic read-head technology, highly sensitive magnetic field sensors and MRAM (magnetoresistive random access memory) devices. For the above mentioned technologies, the EB-effect plays a key role even though a complete description of the microscopic coupling mechanism is still missing. It is widely accepted that the origin of the EB-effect can be traced back to the existence of pinned uncompensated spins (UCS) in the antiferromagnet (AFM) or at its interface. Such UCS have been observed by various experimental techniques. In a simple extension of the model originally proposed by Meicklejohn and Bean, the observed small size of the exchange bias field could be related to pinned UCS. The compensated interfacial spins and the rotating (non-pinned) UCS were found not to contribute to the exchange bias effect. However, the understanding of the underlaying mechanism is still clouded by contradictory reports: For example, both a parallel as well as an antiparallel orientation of the UCS relative to the magnetization direction of the ferromagnet were reported for systems containing the same AFM and FM materials. In this thesis, two different EB-systems were investigated by low-temperature magnetic force microscopy (MFM) and vibrating sample magnetometry (VSM). These complementary experimental techniques allow us to image the spatial distribution, orientation and density of the UCS at nanometer scale (MFM) and to determine their orientation and density in various externally applied magnetic fields (VSM). Different magnetisation histories in magnetometry and MFM measurements are used advantageously to demonstrate the co-existence of pinned UCS that are parallel and antiparallel to the cooling field in metallic (IrMn) and oxidic(CoO) EB-systems. We further conclude that the EB-effect is a result of pinned interfacial UCS, which are antiparallel to the FM spins. The often observed positive vertical shift of the magnetisation loop after field cooling is due to pinned UCS that align parallel to the cooling field, but are of little importance for the EB-effect itself. Furthermore we present a MFM study of an AFM/FM bilayer which, for the first time, reveals that the UCS-density undergoes strong variations on single grain scale. The large variations of the UCS-density observed on single grain scale are explained within a simple statistical approach. The transmission electron microscopy (TEM) images reveal that our sample satisfies the conditions of the model proposed by Takano et al.: sharp grain interfaces with only few crystalline, atomic steps. The small number of steps per grain generates a limited distribution of terrace sizes which leads to poor statistics and as a consequence to a strong local variation of the UCSD, as indeed measured. Quantitatively, three different areas can be distinguished: (1) regions with UCS aligned antiparallel to the FM. (2) regions where no UCS exist. (3) regions with UCS aligned parallel to the FM. Note that the regions (1) dominate such that on average the UCS are aligned antiparallel to the FM spins. It is interesting to see that in an applied field, the FM domains always “retract” to the regions (1), containing the UCS aligned antiparallel to the FM, avoiding the regions (3). The fact that the FM domains retract from these areas suggests that the locations with parallel coupling of the UCS exhibit a reduced exchange coupling strength compared to the antipalallel coupled UCS. In addition, they seem to weaken the overall exchange bias field and are thus defined as anti-biasing regions. Microscopically, the observed anti-biasing regions are explained by a direct coupling between neighbouring AFM grains. TEM images show a wide range of grain boundery tilt-angles. We thus expect in some cases a strong direct coupling between AFM grains (small tilt angles), in others we expect decoupled or weakly coupled grains (large tilt angles). We suggest that a strong direct coupling between neighbouring AFM grains may lead to the observed anti-biasing regions. From this simple picture we conclude that sophisticated grain boundary engineering leading to decoupled AFM grains, is one possible way to increase the EB effect. For instance we propose the co-deposition of Cr and Co for the AFM layer. The segregation of Cr along the boundaries would then lead to decoupled grains. This work may provide guidelines for the design of experiments which correctly determine the densities of those UCS that do contribute to the EB-effect. A considerably improved microscopic understanding of the exchange coupling in polycristalline thin films raises the possibility of an enhancement of the EB-effect by an order of magnitude.