The realm of the nano-world begins when things start getting smaller in size than one thousandth of the thickness of the human hair. Surface patterning at the nanoscale has started to find applications in information storage, self-cleaning of surfaces due to the "lotus effect", biocompatible materials based on surface roughness and many more. Several methods such as particle-beam writing, optical lithography, stamping and various kinds of self-assembly are widely used to serve the purpose of patterning smaller surface structures. However, globally much research is going into developing more efficient, reproducible and simple methods of patterning surfaces and in better controlling the order of these nanostructures. Researchers have always looked upon Nature to get inspiration and to mimic its model in engineering novel architectures. One of the methods used by this greatest artist (Nature) to make beautiful patterns around is through reaction diffusion based non-linear processes. Non-linear systems driven away from equilibrium sustain pattern only during the continuous dissipation of a regular flow of energy and are different from equilibrium processes that are converging towards a minimum in free energy (a. k. a. self-assembly). Dissipative pattern formation from micrometer to kilometers scale has been known but ordered patterns at nanoscale have never been achieved. In the process of thoroughly characterizing suitable substrates for nanoelectronics applications, we came across a remarkable process leading to the formation of highly ordered arrays of dimples on tantalum. The pattern formation happens in a narrow electrochemical windows which are functions of many parameters such as concentration, external applied voltage, temperature etc. After investigating the formation of dimples by performing spatio-temporal studies, we found that the underlying principles behind this unique way of engineering nano-structures have their roots in nonlinear interaction/reaction electro-hydrodynamics. We then have demonstrated the generality of this process by extending it to titanium, tungsten and zirconium surfaces. The pattern similar to Rayleigh-Bernard convection cells originates inside the electrochemical solution due to coupling among electrolyte ions during their migration across the electrochemical double layer (Helmholtz layer) and simultaneously imprints on the surface due to dissolution of metal oxide via etching. Based on these results we further postulate that, given appropriate electropolishing chemistry; these patterns can be formed on virtually any metal or semiconductor surface. The application of these nanostructures as nanobeakers for placing metal nanoparticles is also elucidated Highly porous materials such as mesoporous oxides are of technological interest for catalytic, sensing, optical and filtration applications: the mesoporous materials (with pores of size 2-50 nm) in the form of thin films can be used as membranes due large surface area. In the second part of this thesis, a new technique of making detachable ultrathin membranes of transition metal oxides is presented. The underlying concepts behind the detachment of membranes from the underlying substrate surface are discussed. The control on the size of the pores by modulating the voltage and concentration is also elucidated. The method is generalized by showing the similar detachment behavior on other metal oxide membranes.Thus, the results of this work introduces new techniques of engineering nanostructures on surfaces based on reaction-diffusion adaptive systems and contribute to the better understanding of electrochemical self-organization phenomena due to migration coupling induced electro-hydrodynamics. / Thesis / Doctor of Philosophy (PhD)