This thesis was motivated by the promise that some physical aspects of astrophysical jets and collimation processes can be scaled to laboratory parameters through hydrodynamic scaling laws. The simulation of astrophysical jet phenomena with laser-produced plasmas was attractive because the laser-target interaction can inject energetic, repeatable plasma into an external environment. Novel laboratory simulations of astrophysical jets involved constructing and using the YOGA laser, giving a 1064 nm, 8 ns pulse laser with energies up to 3.7 + 0.2 J. Laser-produced plasmas were characterized using Schlieren, interferometry and ICCD photography for their use in simulating jet and magnetosphere physics. The evolution of the laser-produced plasma in various conditions was compared with self-similar solutions and HYADES computer simulations. Millimeter-scale magnetized collimated outflows were produced by a centimeter scale cylindrically symmetric electrode configuration triggered by a laser-produced plasma. A cavity with a flared nozzle surrounded the center electrode and the electrode ablation created supersonic uncollimated flows. This flow became collimated when the center electrode changed from an anode to a cathode. The plasma jets were in axially directed permanent magnetic fields with strengths up to 5000 Gauss. The collimated magnetized jets were 0.1-0.3 cm wide, up to 2.0 cm long, and had velocities of ∼4.0 × 10⁶ cm/s. The dynamics of the evolution of the jet were compared qualitatively and quantitatively with fluxtube simulations from Bellan's formulation [6] giving a calculated estimate of ∼2.6 × 10⁶ cm/s for jet evolution velocity and evidence for jet rotation. The density measured with interferometry was 1.9 ± 0.2 × 10¹⁷ cm^-3 compared with 2.1 × 10¹⁶ cm^-3 calculated with Bellan's pressure balance formulation. Kinks in the jet column were produced consistent with the Kruskal-Shafranov condition which allowed stable and symmetric jets to form with the background magnetic fields. The Euler number for the laboratory jet was 9 compared with an estimate of 40 for young stellar object jets [135] which demonstrated adequate scaling between the two frames. A second experiment was performed concerning laboratory simulations of magnetospheres with plasma winds impinging on permanent magnetic dipoles. The ratio of the magnetopause measured with ICCD photography to the calculated magnetopause standoff distance was ∼2.