Current state-of-the art explicit-solvent atomistic molecular dynamics (MD) simulations are reviewed. We describe the basic principles and limitations of MD methodology. We also explain how to compare MD simulations with experiments and how to correctly interpret MD data. Different types of simulation approaches are introduced. We start with standard simulations and then continue with techniques which allow one to a certain extent overcome sampling limitations and derive free energies: replica-exchange methods, collective-variable based methods such as metadynamics, alchemical methods, Markov state models and continuum solvent approach. We emphasize explaining the limitations of the methods, in order to avoid over-interpretation of the simulation data. Then we introduce recent progress in the force fields that are used for simulations of quadruplexes. Finally, two specific areas are reviewed. First, we explain how MD simulations are essential to unravel the uniqueness and complexity of quadruplex folding landscape, what are the basic consequences and hallmarks of kinetic partitioning of the landscape and why low-dimensionality descriptions (both experimental and computational) can easily lead to major oversimplifications. Second, MD simulations-based recent approaches to probe quadruplex-ligand interactions are discussed. The review is primarily written for readers who are not advanced experts in MD simulations, with the aim to openly expose their limitations.