In this thesis, we study the surface of water in its liquid and solid state. We investigate (i) an aqueous system where a model membrane interacts with amphiphilic dendrimers and (ii) single crystalline ice. We present a molecular scale description of both systems. To this end, we use sum frequency generation (SFG) spectroscopy, which provides unique information on the vibrational response of the outermost molecules of surfaces. Amphiphilic polyphenylene dendrimers (PPDs) are macromolecules with well-defined functional groups at the surface. They can be used as drug carriers in biological systems. We systematically study the interactions between PPDs with different surface termination, and a model membrane. We find that PPDs with linear alkyl chains as functional groups are more favorable to bind with the model membranes. They also have better cellular uptake in comparison with branched alkyl groups and PPDs that only have hydrophilic functionalities. PPDs with different hydrophilic groups (a carboxylic acid instead of a sulfonic acid) have similar surface activities at the model membrane-air interface, as well as similar cell penetrating properties. These findings indicate that the PPD-cell membrane interactions are dominated by the hydrophobic chains. Furthermore, we observe that larger PPDs disorganize the lipid monolayer, while smaller ones organize it. Cell uptake results show that smaller PPDs have better cell penetration than larger ones, possibly because the larger PPDs disorganize the cell membrane. We surmise that an ideal pyrene core dendrimer with good cell uptake properties has amphiphilic functionalities, with hydrophilic and linear alkyl functional groups. In the second part of the thesis, we study the quasi-liquid layer (QLL), which is present on ice even below the freezing point, as recognized by Faraday over 150 years ago. This layer is important for surface chemistry and glacier sliding close to subfreezing conditions. We grow single crystalline ice samples from a crystalline seed which is pulled out slowly from a liquid water melt. The samples are subsequently characterized with cross polarisers, Formvar etching, X-ray diffraction as well as SFG spectroscopy. Experimentally, while heating the ice sample, starting at 235 K, a rather abrupt blue shift of the frequency of the OH stretch modes of hydrogen bonded interfacial water molecules is observed at 257 K. This points to an abrupt weakening of the hydrogen bonding structure at the interface. From a comparison of the experiments with simulations, we conclude that the QLL melts in a discrete manner, from one to two bilayers at 257 K. Furthermore, the SFG spectra indicate that at 269 K, the QLL has more characteristics of ice than of liquid water. Time resolved SFG experiments on single crystalline ice show that the vibrational relaxation dynamics of interfacial ice water molecules is faster than for the liquid water-air interface, similar to what has been reported in the literature for bulk ice and water. We found timescales of around 70 fs vs 200 fs, for ice and liquid respectively. Finally, a study of the proton transfer in ice is described. An experimental approach is suggested to produce single crystalline HCl-doped ice, and to obtain information on the proton transfer in- and on the surface of ice, employing SFG and time domain terahertz spectroscopy.