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Josephson junctions (JJs) are an integral component in quantum computing, low temperature electronics, and fundamental physics research. Hybrid superconductor-semiconductor JJs in two-dimensional materials have recently emerged as a paradigm for novel applications, harnessing gate-tunable supercurrents and strong spin-orbit coupling in a scalable platform. In this thesis, we present a detailed study of planar JJs in an InAs/Al heterostructure, when subjected to bias currents, microwave irradiation and in-plane magnetic fields. First, we investigate the stochastic dynamics of the superconducting-to-resistive transition of planar JJs and superconducting quantum interference devices (SQUIDs). We find that dynamics at low temperature are dominated by quantum fluctuations in the superconducting phase, which suppress the switching current to values less than half of the critical current. Phase dynamics are altered in a SQUID, such that the switching current of a JJ is more than doubled in a SQUID relative to being in isolation. Moderate damping leads to phase diffusion at higher temperatures, with a transition temperature that is tunable with gate voltages, magnetic fields and fluxes threading the SQUID. In a second experiment, we perform tunnelling spectroscopy measurements on a planar JJ irradiated by a microwave signal. Replicas in the conductance spectrum are shown to be consistent with photon assisted tunnelling (PAT) between the spectroscopic probe and Andreev bound states (ABSs) in the junction, rather than due to novel light-matter coupling in the form of Floquet-Andreev states. By tuning the tunnel-barrier transparency and Fermi energy with gate voltages, in addition to complementary current-phase relation (CPR) measurements, signatures unique to PAT are identified. Further, microwave-induced distortions to the CPR are shown to be consistent with a non-equilibrium occupation of ABSs, without invoking Floquet states. Finally, supercurrent and tunnelling spectroscopy measurements are performed on planar JJs in an in-plane magnetic field. Phase shifts in the CPR are reported relative to a phase reference, in devices with different superconducting lead sizes to investigate orbital effects. At low fields, we observe gate-dependent phase shifts of up to φ=0.5π, consistent with a Zeeman field coupling to highly-transmissive ABSs via Rashba spin-orbit interaction. A distinct phase shift at larger fields is concomitant with a switching current minimum and a closing and reopening of the superconducting gap. These signatures of a phase transition, which might resemble a topological transition, scale with the superconducting lead size indicating the crucial role of orbital effects in planar JJs. Our results give a new baseline understanding of planar JJs in InAs/Al heterostructures, and elucidate the interplay of Zeeman, spin-orbit and orbital effects in magnetic fields. This guides towards improved realisations of gate-tunable qubits, superconducting electronic.