The fundamental properties of computed flow fields using particle imaging velocimetry (PIV) have been investigated, viewing PIV processing as a black box without going in detail into algorithmic details. PIV processing can be analyzed using a linear filter model, i.e. assuming that the computed displacement field is the result of some spatial filtering of the underlying true flow field given a particular shape of the filter function. From such a mathematical framework, relationships are derived between the underlying filter function, wavelength response function (MTF) and response to a step function, power spectral density, and spatial autocorrelation of filter function and noise. A definition of a spatial resolution is provided independent of some arbitrary threshold e.g of the wavelength response function and provides the user with a single number to appropriately set the parameters of the PIV algorithm required for detecting small velocity fluctuations. The most important error sources in PIV are discussed and an uncertainty quantification method based on correlation statistics is derived, which has been compared to other available UQ-methods in two recent publications (Sciacchitano et al. 2015; Boomsma et al. 2016) showing good sensitivity to a variety of error sources. Instantaneous local velocity uncertainties are propagated for derived instantaneous and statistical quantities like vorticity, averages, Reynolds stresses and others. For Stereo-PIV the uncertainties of the 2C-velocity fields of the two cameras are propagated into uncertainties of the computed final 3C-velocity field. A new anisotropic denoising scheme as a post-processing step is presented which uses the uncertainties comparing to the local flow gradients in order to devise an optimal filter kernel for reducing the noise without suppressing true small-scale flow fluctuations. For Stereo-PIV and volumetric PIV/PTV, an accurate perspective calibration is mandatory. A Stereo-PIV self-calibration technique is described to correct misalignment between the actual position of the light sheet and where it is supposed to be according to the initial calibration procedure. For volumetric PIV/PTV, a volumetric self-calibration (VSC) procedure is presented to correct local calibration errors everywhere in the measurement volume. Finally, an iterative method for reconstructing particles (IPR) in a volume is developed, which is the basis for the recently introduced Shake-the-Box (STB) technique (Schanz et al. 2016).@en