The hydrogen bond is one of the most important and interesting phenomena in nature. In this publication we will shed light on the discovery of hydrogen bond and a time evolution of its definition in the last 100 years. Both structural and spectroscopic parameters of the hydrogen bond will be discussed. A special focus will be given to the latest IUPAC definition of the hydrogen bond and its consequences to scientific research. The main aim of this study is to highlight theoretical studies based on first principles calculations and molecular dynamics simulations which not only support experimental results but also provide parameters which are crucial to understand the nature of hydrogen bonds. Particular attention will be given to methods and theoretical ideas used in the computational studies of hydrogen bonds. Utilizing static DFT/ab initio calculations and molecular dynamics simulations enables comparison of different binding energies and studying time evolution of the hydrogen-bonded molecular system on the atomistic level. We will discuss time-resolved properties of weak intermolecular hydrogen bonds, using as an example C-H…F containing model systems, namely F3CH*(HF)n molecular complexes and (F3CH)2-4 aggregates.