Laser diagnostics have been a staple for experimental combustion research as a modern tool to evaluate high temperature reacting flow environments and to contribute to the fundamental knowledge needed for improving our current combustion systems in a non-intrusive way; they also represent an essential tool for validating computational models. High pressure diagnostics are of particular importance due to the fact that the majority of practical combustion systems operate at high pressure, involving increased challenges in the measurements. The current work examines a variety of linear and non-linear light/matter interaction processes (Raman, fluorescence, and coherent anti-Stokes Raman spectroscopy or CARS) with the goal of measuring the temperature, pressure, and spatial distribution of important reacting flow species. The specific techniques involving OH planar laser induced fluorescence (PLIF), two-line OH PLIF thermometry, two-photon CO PLIF, nanosecond vibrational CARS and hybrid femtosecond/picosecond rotational CARS are all demonstrated at atmospheric pressure using a non-premixed coflow impinging jet as a study flame and examined in detail under high pressure conditions (up to 12 bar) as a coflow flame and in a calibration high pressure vessel; the implications of pressure are discussed in detail in the linear and non-linear techniques. The high pressure experimental data set shows soot laser induced incandescence (LII) as a source of interference for high pressure LIF in non-premixed flames, good agreement with 3 different chemical mechanisms, in particular at high pressure, between an OpenFOAM simulated fluorescence and the experimental pressure dependent data regarding both the spatial distribution of the OH molecule and the overall number of $OH$ molecules interacting with the excitation source. Chirp is identified as a critical parameter when using a second harmonic bandwidth compressor in the hybrid fs/ps CARS configuration, and the chirped CARS signal depends strongly on probe delay in N2 experiments. High quality high pressure data can be achieved once chirp influence has been quantified accurately. Together the combination of diagnostics studied provide insights into high pressure laser diagnostics challenges beyond what is currently available.