De, ArinjoyQuantum simulation is perhaps the most natural application of a quantum computer, where a precisely controllable quantum system is designed to emulate a more complex or less accessible quantum system. Significant research efforts over the last decade have advanced quantum technology to the point where it is foreseeable to achieve `quantum advantage' over classical computers, to enable the exploration of complex phenomena in condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. While the realization of a universal fault-tolerant quantum computer remains a future goal, analog quantum simulators -- featuring continuous unitary evolution of many-body Hamiltonians -- have been developed across several experimental platforms. A key challenge in this field is balancing the control of these systems with the need to scale them up to address more complex problems. Trapped-ion platforms, with exceptionally high levels of control enabled by laser-cooled and electromagnetically confined ions, and all-to-all entangling capabilities through precise control over their collective motional modes, have emerged as a strong candidate for quantum simulation and provide a promising avenue for scaling up the systems. In this dissertation, I present my research work, emphasizing both the scalability and controllability aspects of \ion based trapped-ion platforms, with an underlying theme of analog quantum simulation. The initial part of my research involves utilizing a trapped ion apparatus operating within a cryogenic vacuum environment, suitable for scaling up to hundreds of ions. We address various challenges associated with this approach, particularly the impact of mechanical vibrations originating from the cryostat, which can induce phase errors during coherent operations. Subsequently, we detail the implementation of a scheme to generate phase-stable spin-spin interactions that are robust to vibration noise. In the second part, we use a trapped-ion quantum simulator operating at room temperature, to investigate the non-equilibrium dynamics of critical fluctuations following a quantum quench to the critical point. Employing systems with up to 50 spins, we show that the amplitude and timescale of post-quench fluctuations scale with system size, exhibiting distinct universal critical exponents. While a generic quench can lead to thermal critical behavior, a second quench from one critical state to another (i.e., double quench) results in unique critical behavior not seen in equilibrium. Our results highlight the potential of quantum simulators to explore universal scaling beyond the equilibrium paradigm. In the final part of the thesis, we investigate an analog of the paradigmatic string-breaking phenomena using a quantum spin simulator. We employ an integrated trapped-ion apparatus with $13$ spins that utilizes the individual controllability of laser beams to program a uniform spin-spin interaction profile across the chain, alongside 3-dimensional control of the local magnetic fields. We introduce two static probe charges, realized through local longitudinal magnetic fields, that create string tension. By implementing quantum quenches across the string-breaking point, we monitor non-equilibrium charge evolution with spatio-temporal resolution that elucidates the dynamical string breaking. Furthermore, by initializing the charges away from the string boundary, we generate isolated charges and observe localization effects that arise from the interplay between confinement and lattice effects.enDissertationQuantum physicsAtomic physicsCondensed matter physicsLattice Gauge TheoryMany-body physicsNon-equilibrium DynamicsQuantum ComputingQuantum SimulationTrapped-ions