Giant molecular clouds (GMCs), out of which stars form, are complex, dynamic systems, which both influence and are shaped by the process of star formation. In this dissertation, I examine three different facets of the dynamical motions within GMCs. Collapse modes in different dimensional objects. Molecular clouds contain lower dimensional substructures, such as filaments and sheets. The collapse properties of finite filaments and sheets differ from those of spherical objects as well as infinite sheets and filaments. I examine the importance of local collapse modes of small central perturbations, relative to global collapse modes, in different dimensional objects to elucidate whether strong perturbations are required for molecular clouds to fragment to form stars. I also calculate the dependence of the global collapse timescale upon the aspect ratio of sheets and filaments. I find that lower dimensional objects are more readily fragmented, and that for a constant density, lower dimensional objects and clouds with larger aspect ratios collapse more slowly. An edge-driven collapse mode also exists in sheets and filaments and is most important in elongated filaments. The failure to consider the geometry of a gas cloud is shown to lead to an overestimation of the star formation rate by up to an order of magnitude. Molecular tracers of turbulent energy dissipation. Molecular clouds contain supersonic turbulence that simulations predict will decay rapidly via shocks. I use shock models to predict which species emit the majority of the turbulent energy dissipated in shocks and find that carbon monoxide, CO, is primarily responsible for radiating away this energy. By combining these shock models with estimates for the turbulent energy dissipation rate of molecular clouds, I predict the expected shock spectra of CO from molecular clouds. I compare the results of these shock models to predictions for the emission from the unshocked gas in GMCs and show that mid-to-high rotational transitions of CO (e.g., J = 8 to 7), should be dominated by shocked gas emission and should trace the turbulent energy being dissipated in molecular clouds. Orion-Eridanus superbubble. The nearby Orion star forming region has created a large bubble of hot plasma in the local interstellar medium referred to as the Orion-Eridanus superbubble. This bubble is unusual in that it is highly elongated, is believed to be oriented roughly parallel to the galactic plane, and contains bright filamentary features on the Eridanus side. I fit models for a wind driven bubble in an exponential atmosphere to the Orion-Eridanus superbubble and show that the elongation of the bubble cannot be explained by such a model in which the scale height of the galactic disk is the typical value of 150 pc. Either a much smaller scale height must be adopted or some additional physics must be added to the model. I also show that the Eridanus filaments cannot be equilibrium objects ionized by the Orion star forming region. / Graduate / 0606 / andyrpon@gmail.com