This work is devoted to theoretical studies of transport and heating in toroidal confinement devices and to the development of new numerical methods and fast codes. The proper description of transport and heating is one of the main tasks of fusion plasma theory. Within our group, these activities focus on the following topics: 1. Neoclassical theory of plasma transport in stellarators: Evaluation of non-axisymmetric and axisymmetric transport coefficients and of bootstrap current; optimization of devices with respect to neoclassical transport; calculation of the generalized Spitzer-Härm function, which is necessary for evaluation of current drive in stellarators, in general collisionality regimes. 2. Theory and modelling of particle transport in stellarators including cases where the diffusion approximation of neoclassical theory may be violated: e.g., convective particle transport; transport in general magnetic field topologies in toroidal confinement devices - islands, ergodic layers. 3. Theory and modelling of nonlinear electron cyclotron resonance heating (ECRH) and current drive (ECCD) in tokamaks and stellarators, study of neoclassical tearing mode stabilization methods by means of ECCD. 4. Theory and modelling of magnetic field penetration and plasma transport in edge plasmas of devices with general three dimensional geometry of the magnetic field (DED of TEXTOR, W7-X). All these topics are linked to each other with respect to subject and methodology. The use of local magnetic coordinate systems and of the multiple coordinate system approach proved to be a key point in the development of fast and effective numerical tools at ITP Graz as well as at IPP Greifswald.