Microwave Kinetic Inductance Detectors (MKIDs) are remarkable photon detectors, that have single photon detection and energy resolving capabilities in the near-infra red and higher frequency range. At lower frequencies, MKIDs are excellent radiation detectors as well, because of their high sensitivity and natural multiplexing capabilities, which enable large scale detector arrays.In the (near) optical regime, MKIDs can use their single photon energy resolving capabilities for direct exoplanet detection, in missions like Hab-Ex or LUVOIR. This would enable atmospheric characterization, potentially finding habitual exoplanets. However, two aspects of the MKID still need improvement for this application: the photon absorption efficiency must go from 30% to 50% and the resolving power must go from 8 to 100, both for wavelengths of 1 µm. In this thesis, we study the single photon response and generation-recombination (GR) noise in optical NbTiN-Al hybrid MKIDs, to find knowledge gaps and opportunities to improve detector performance. For the single photon response, we set up a model starting from the Rothwarf-Taylor and Mattis-Bardeen equations, including the pair-breaking efficiency as only fit parameter. Both at high (220 mK and 250 mK) and low (120 mK) temperatures, the model predicted the single photon response of 4 different wavelengths correctly, with a fitted pair-breaking efficiency close to expected values (30%-70%), but somewhat high, which might be due to a non-thermal distribution of quasiparticles caused by read power. In particular, the effect of phonon trapping was captured by the model, which was verified by considering MKIDs on substrate and membrane.At lower temperatures (120 mK), a second exponential decay in both the amplitude and phase single photon pulse tail was observed, which is not explained by the model. This second decay was faster for higher read powers. For the GR noise, also an unexpected feature was observed: the GR noise level dropped exponentially, when lowering temperature (<250 mK), for the amplitude, phase and cross power spectral densities (PSDs). High read powers mask this effect, due to the creation of excess quasiparticles. The noise drop was present in all analysed MKIDs, except for an MKID with an 150 nm (instead of 50 nm) thick Al film, which might be due to read power induced excess quasiparticles. When assuming the GR noise to be Poissonian, we show that the behaviour could be explained by a process which limits the quasiparticle lifetime, while keeping the quasiparticle density thermal.We hypothesize the cause of both of these unpredicted measurements to be quasiparticle trapping, which is the localisation of quasiparticles. This process is known to degrade superconducting tunnel junction detectors and limit quasiparticle lifetimes in MKIDs. A secondary ion-mass spectroscopy (SIMS) analysis showed Fe contamination on the substrate-Al film interface, which is thought to be the quasiparticle trapping cause in our systems, consistent with the observation that increasing the film thickness diminishes the GR noise drop. To our knowledge, quasiparticle trapping has not be studied in steady state experiments, such as GR noise measurements.Different models including quasiparticle trapping have been set up and can predict the amplitude PSDs, when assuming that trapped quasiparticles cannot dissipate microwave power. However, comparison of the fitted model parameters with the trapping and detrapping rates calculated by Kozorezov et al., showed a orders of magnitude difference. Combining this with the fact that amplitude, phase and cross PSDs show similar behaviour, implying that they relate to Cooper-pair fluctuations, led us to conclude that the trapping process cannot be the cause of the observed behaviour. On-trap recombination most likely plays a role in the GR noise drop, but models including this process involve cyclic transitions and non-equilibrium steady states, greatly complicating the calculations. The second exponential decay could not be described by the trapping models, but also here on-trap recombination and Cooper-pair fluctuations must be considered.A qualitative analysis on the MKID detector performance (both single photon and radiation power integration) showed that quasiparticle trapping effects can increase the energy resolving power and noise equivalent power at low temperatures, when this effect replaces the usual lifetime saturation due to excess quasiparticles.