In this thesis, we explore superfluidity and phase coherence of weakly interacting Bose gases using analytical and c-field simulation methods. We first investigate superfluidity of the Bose-Einstein condensate (BEC) phase of a three dimensional (3D) gas of 6Li molecules by stirring it with a Gaussian potential. This is motivated by experiments in ultracold atoms, where superfluidity is probed by laser stirring. We determine the induced heating rate due to stirring potential using analytical and simulation methods. The heating rate increases steeply above a velocity vc, which we define as the critical velocity. Below this velocity, the moving potential creates negligible heating. For an idealized case of a homogeneous condensate at low temperature stirred along a linear path the onset of dissipation occurs at a vc, which is equal to the Bogoliubov prediction of the phonon velocity vB. This is consistent with the Landau criterion of superfluidity, which predicts vB as the critical velocity vc. However, for an experimental setting of a trapped gas at an intermediate temperature stirred along a circular path the onset of dissipation occurs at a vc below the phonon velocity vB. We show that this reduction of vc is due to the finite temperature, the circular instead of linear stirring motion, and the inhomogeneous density of the cloud. With our analytical and simulated vc we show a quantitative comparison of the measured vc on the BEC side of the BEC-BCS crossover of the experiment performed in the Moritz group [Phys. Rev. Lett. 114, 095301 (2015)]. We then investigate the superfluid to thermal transition of a 2D Bose gas of 87Rb atoms in a trap using dynamical c-field methods. We stir the trapped cloud with a repulsive stirring potential along a circular path around the trap center. By choosing different radii for the circular motion we stir the cloud in different phase-space density regions. We identify the superfluid, the crossover, and the thermal regime by a nonzero, a sharply decreasing, and a zero critical velocity vc, respectively. We find the observed crossover regime to be consistent with the prediction for the Kosterlitz-Thouless (KT) transition in a homogeneous gas. However, this is in contrast with the experiment performed in the Dalibard group [Nat. Phys. 8, 645 (2012)], in which a non-trivial shift of the crossover regime is observed. We show that the origin of that shift is the absence of thermal equilibrium between the superfluid and the thermal parts of the cloud. We demonstrate that the equilibration process of the system occurs on a timescale of seconds, which is an order of magnitude longer than the used hold time of 0.1 s in the experiment. We show that this slow equilibration is due to a slow relaxation of vortices which carry the stirring-induced energy out of the superfluid into the thermal cloud of the system. We then examine the phase coherence of a homogeneous 2D gas of 87Rb atoms using short time-of-flight expansions. During the expansion, in situ phase fluctuations evolve into density fluctuations. We analyze noise correlations of these density fluctuations, below and above the KT transition. Below the transition, noise correlations are oscillatory and their magnitude is controlled by the scaling exponent of the quasi-condensed phase. However, above the transition this oscillatory behavior vanishes quickly after a short expansion time. We point out that the magnitude and the shape of noise correlations can be used to identify the KT transition in an experiment. Furthermore, we derive an analytic expression for the spectrum of noise correlations below the transition, which we propose to use to determine the scaling exponent of the quasi-condensed phase experimentally. We present and discuss the experiment in the Moritz group, in which noise correlations are used to determine the phase coherence of a 2D bosonic system of 6Li molecules.