Full waveform inversion is a tool to obtain high-resolution property models of the subsurface from seismic data. However, the technique is computationally expens- ive and so far no multi-dimensional implementation exists to achieve a resolution that can directly be used for seismic interpretation and characterisation. In this thesis we discuss a method to overcome some of the current limitations of seismic full waveform inversion. The scheme consists of alternating local linear inversions followed by global nonlinear total field estimations. By backpropagating sources and receivers from the acquisition surface into the subsurface, the inversion process can be localised. Inversion of backprogated data to obtain the properties in a local domain only, is a much smaller problem com- pared to direct inversion of surface data, aiming at the properties of the full subsurface at once. As a result we can use the full frequency spectrum, up to 55 Hz and beyond, to obtain property models with a resolution that is compar- able to the one obtained by conventional structural imaging. A high-resolution global subsurface model in terms of properties is then obtained by combining many of these local results. Because all local inversions are fully independent, the scheme is extremely suitable for parallelisation. In the first iteration we assume that the wavefields are propagating in a smooth background model only. Obtaining a high-resolution property model by localised inversion, showing structural features of the subsurface, tells us that wavefield propagation in a smooth background is not a good approximation. This is why in a next step we perform a total wavefield estimation based on the latest combined local inversion results. In this way the full nonlinear relationship between the measured seismic data and the subsurface properties is utilised. We show how nonlinear wavefield effects as multiple scattering, transmission and true travel- times in the inverted medium, can properly be estimated and how they can be used to obtain significantly improved subsurface models. Examples are given where nonlinear full waveform inversion allows us to recover structural informa- tion, particularly very steep dipping geology, that can never be imaged by using a linear data model. It is demonstrated that by using the nonlinear relationship between the measured data and the obtained subsurface properties, the resolution can be increased even further. Full waveform inversion as proposed in this thesis, allows reconstruction of subsurface models with a spatial resolution that goes beyond the equivalent temporal frequencies in the measured seismic data. Consequently, estimation of absolute quantitative properties from a bandlimited seismic signal becomes pos- sible. It is discussed that every scatterer in the subsurface introduces a coda that will have an effect on the imaging of the deeper subsurface. Especially the near- surface can introduce nonlinearity, particularly in terms of multiple scattering, which makes imaging the deeper area of interest, e.g. a reservoir, difficult. In this thesis we show how these internal multiples cannot only be handled, but also how they can contribute to the inversion process by introducing enhanced illumination. The method is first derived in 2-D under the acoustic approximation and assum- ing a constant and known density. Since current implementation of the scheme requires homogeneous background models as input to the inversion, in 2-D the method is demonstrated on synthetic datasets only. Field data application using a 2-D data model needs extension to inhomogeneous background models and to true elastic inversion, which is in principle straightforward, but has not been im- plemented yet. In this thesis we perform these extensions for the 1.5-D case, assuming a ho- rizontally layered subsurface per CMP location. Nonlinear elastic full waveform inversion, aiming at the recovery of three elastic parameters over a reservoir se- quence, is applied to synthetic data as well as to a field dataset from the Middle East. It is shown that nonlinear full waveform inversion is suitable for reservoir characterisation while increased resolution and better results in terms of quantit- ative properties are obtained.