The velocity fields of high Reynolds number, turbulent, wall boundary layers in non-equilibrium pressure gradients are experimentally investigated. Experiments in two wall configurations were performed; one with a hydrodynamically smooth test wall composed of flat aluminum panels, and the other with a rough surface consisting of 2 mm tall, staggered, circular cylindrical elements. A representative set of pressure gradient distributions were generated on the research wall by a systematically rotated NACA 0012 airfoil placed in a wind tunnel section to determine the functional dependence of the boundary layer formation on pressure gradient. Particle image velocimetry (PIV) was the primary measurement technique used to determine time-resolved features of the velocity flow field. newline{}newline{} It is shown that regardless of wall condition and Reynolds number, the non-equilibrium turbulent boundary layers exhibit increasingly non-local behavior with streamwise development. This is apparent as a lag to the pressure gradient distribution observed in the streamwise developing integrated boundary layer parameters. These ``history effects" are also prevalent in mean velocity profiles which are exhibited as a cross-over of the favorable and adverse pressure gradient profiles in the logarithmic layer. Similar cross-over points are observed in the Reynolds shear and normal stresses, particularly at the streamwise station downstream of the pressure gradient switch. The primary effect of the rough wall is to increase the magnitude of flow scales, and, while they exhibit the same qualitative history effects as the smooth wall, the rough wall flows show an earlier relaxation to equilibrium. Despite inherent uncertainties of indirect skin friction methods for the rough wall, the effective sandgrain roughness parameter k_s does not show a functional dependency to pressure gradient history. An evaluation of the wall-similarity hypothesis solely based on boundary layer thickness to roughness parameter ratios delta/k_s is insufficient and additional parameters such as pressure gradient histories, local roughness Reynolds numbers, and bias uncertainties due to instrument spatial resolution must be considered. / Doctor of Philosophy / In the interface between a surface and a moving fluid is the boundary layer where high shear and viscous stresses cause the bulk velocity to decrease to zero. When turbulent, this region of fluid is characterized by random, chaotic, and fluctuating motions of varying sizes. Parameters such as pressure gradients and geometric irregularities of the surface, referred to as roughness, can increase fluctuating pressures and velocities within the boundary layer and cause unwanted noise, vibration, and increased drag. Although many studies have evaluated boundary layers with either roughness or pressure gradient independently, most surfaces in practical application are susceptible to the compounding influences of both of these parameters. Thus, it is necessary to expand the current knowledge database to include complex flow fields necessary to improve data driven modeling and vehicle design.newline{}newline{} This study focuses on experimental observations of the turbulent velocity field developing in both a rough and smooth wall boundary layer that is induced to a family of bi-directional pressure gradients generated by the pressure field of a rotating airfoil inside in a wind tunnel. Through statistical observations of the velocity field it was found that the varying pressure gradients caused the flow to develop non-local dependencies such that the response of the downstream boundary layer was dependent on the upstream flow history. The principal effect of roughness was to increase the magnitude of turbulent scales, but to show the same qualitative response to the pressure gradient history as seen in a smooth wall flow. However, direct comparison of rough and smooth wall turbulence statistics by means of the ``wall-similarity hypothesis" requires careful consideration of multiple parameters including these flow histories, scales prescribed by roughness parameters, and bias errors from experiment under-resolution of the velocity field.