In the present work we use analytical and computational methods in order to examine different dynamical scales in the solar atmosphere and the solar wind. The latter represents the expansion of the atmosphere to large radial distances, further than the Earth's orbit. After the introduction presented in chapter 1, we start our analysis with investigating and presenting potential force-free field extrapolations based on observational input for the photospheric magnetic field from different instruments, namely GONG and MDI, at different resolutions. More specifically, we have developed a Potential Field Source Surface (PFSS) module as a part of the computational code MPI-AMRVAC in three dimensions in spherical coordinates using the decomposition method of the spherical harmonics. A source surface is assumed at a heliocentric distance of $2.5R_\odot$. This module can be used to estimate the three-dimensional global magnetic field information corresponding to different Carrington Rotations and synoptic magnetograms, as initial condition for coronal and solar wind models. We examine in chapter 2 both global (PFSS) and local (Green-function-based potential field) extrapolation schemes on spherical and Cartesian grids, respectively. A comparison is performed for the active region AR10756 of the Carrington Rotation CR2029 corresponding to April-May 2005 between the two extrapolation techniques. The local extrapolation method has a less dominant open field topology, as there is no source surface in that model taken into account, while the curvature is neglected contrary to the global PFSS model. We continue in chapter 3 presenting numerical simulations in 3D settings where coronal rain phenomena take place in a magnetic configuration of a quadrupolar arcade system in a stratified atmosphere from chromospheric to coronal heights. Our simulation is a magnetohydrodynamic simulation including anisotropic thermal conduction, optically thin radiative losses, and parametrized heating as main thermodynamical features to construct a realistic arcade configuration from chromospheric to coronal heights. The plasma evaporation from chromospheric and transition region heights eventually causes localized runaway condensation events and we witness the formation of plasma blobs due to thermal instability, that evolve dynamically in the heated arcade part and move gradually downwards due to interchange type dynamics. Unlike earlier 2.5D simulations, in this case there is no large scale prominence formation observed, but a continuous coronal rain develops which shows clear indications of Rayleigh-Taylor or interchange instability, that causes the denser plasma located above the transition region to fall down, as the system moves towards a more stable state. Linear stability analysis is used in the non-linear regime for gaining insight and giving a prediction of the system's evolution. After the plasma blobs descend through interchange, they follow the magnetic field topology more closely in the lower coronal regions, where they are guided by the magnetic dips. In chapter 4 we constrain a kinetic solar wind model with Kappa-distributed electrons using observation-driven magnetohydrodynamic (MHD) modeling and in-situ data. Solar wind modeling efforts are presented using an MHD - based as well as a kinetic approach. In the fluid approach, photospheric magnetograms serve as observational input in semi-empirical coronal models that are used for estimating the plasma characteristics up to a heliocentric distance of 0.1AU. From there on a full MHD model which computes the three-dimensional time-dependent evolution of the macroscopic variables of the solar wind up to the orbit of the Earth is exploited. We compare with the results of a kinetic exospheric solar wind model based on the assumption of Maxwell and Kappa velocity distributions functions for protons and electrons respectively. The appropriate boundary conditions are determined to obtain the best comparison with available observations at the Earth's orbit. This provides physical insight on more detailed processes, such as coronal heating and solar wind acceleration, that naturally arise by inclusion of suprathermal electrons in the model. We are interested in the profile of the solar wind speed and density at 1 AU, in characterizing the slow and fast source regions of the wind and in comparing the features of that with results of exospheric models in similar conditions. We start from similar boundary conditions at 0.1AU and propagate the solution up to 1AU to compare MHD and kinetic treatments with observations. On top of that, following the reverse process starting from observations at 1AU and assuming kappa velocity distribution functions for the electrons we improve the close-to-sun boundary conditions to be used in both models to improve future space weather predictions.