This thesis emerges from a patented idea to utilize intentionally structured sur- faces and differences in adsorption strengths to self-assemble some source mate- rial into nanoelectronic components, and ends up in the heated debate regarding structure of ambient water . It investigates the role and relevance of van der Waals (vdW) forces in molecular surface adsorption and water through density- functional theory (DFT), using the exchange-correlation functional vdW-DF [Dion et al., Phys. Rev. Lett. 92, 246401 (2004)] and developments based on it. Results are first computed for adsorption with vdW forces of, e.g., benzene on Au(111) and other coinage metals, phenol on nickel, and graphene on Co, Ni, Pd, Ag, Au, Cu and Pt surfaces. The vdW forces are ubiquitous but for transition metals and on structured surfaces, with defects, incl. The vdW adsorbate attraction benefits from the two-dimensional extent of the surface and favors adsorption sites close to the surface, while the Pauli repulsion keeps the adsorbate away. Impurities, like an adatom or an adsorbed pyramid, pushes the adsorbate away from surface, giving a reduction of the attraction due to vdW forces. In this way the vdW force varies on an atomic scale, and in the weak-adsorption limit coordination rules for adsorption are affected. The thesis illustrates this force competition by varying adsorption site and substrate to find examples where the rule of under-coordination which holds according to DFT without vdW forces, does not when accounting for vdW. An evaluation of the vdW-DF method is made by comparison with a detailed ex- perimentally determined physisorption-potential for H2 on Cu(111). The vdW- DF2 potential-energy curves appear to have an agreement at large with the measured curve. Competition between different kinds of forces rules also other systems. For instance, in water complexes hydrogen bonds compete with vdW force, just like chemisorptive forces due to d-electrons do on transition metals. Bond lengths are shorter than those for typical vdW bonds also here, making both adsorption and water call for improved exchange functionals. DFT calculations are performed for water dimer and hexamer, and for liquid water. Calculations on four low-energetic isomers of the water hexamer show that the vdW-DF accurately determines the energetic trend on these small clusters. How- ever, the dissociation-energy values with the vdW-DF functional are too small, as the exchange approximation used is too repulsive. With the vdW-DF and other functionals that account for vdW forces, the total isomer energies are minimized in molecular configurations, which are compact, and in which many hydrogen bonds (HBs) can be described as distorted, or even as broken. The hexamer experience of the criteria and effects of vdW forces can be used in interpretation of results of molecular dynamics (MD) simulations of ambient water, where vdW forces qualitatively result in liquid water with fewer, more distorted HBs. This is interesting as there is currently a heated debate in the water community on the level of HB distortion in ambient water, and where MD simulations without first principles vdW forces have played an important role to suggest that liquid water is almost tetrahedral, with few distorted HBs. Simula- tions with improved vdW-DF functionals, called vdW-DF2 and optPBE-vdW, result in a structure similar to the HDL phase (high-density liquid) under proper conditions, and thus show that vdW forces may be vital in the two-liquid model suggested in http://www.sciencemag.org/content/304/5673/995.abstract.