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The current complementary metal–oxide–semiconductor (CMOS) technologies are facing greater-than-ever challenges as the Moore’s law approaches to its physical limits. The search for future electronic devices began decades ago. Spintronics, which utilizes the properties of electron spins, is indeed one of the most promising solutions for the beyond-CMOS era. Over the past years, spintronics has been very successful in Hard-disc drives (HDDs) and has significantly increased the storage areal-density. Recently, because of its built-in non-volatility, spintronics has also demonstrated its potential in memory applications. On the other hand, graphene, which is a monolayer of carbon atoms arranged in hexagonal order, is very attractive as the material for spin transport. For example, graphene has the longest spin diffusion length and spin lifetime at room temperature. Therefore, as the device that combines the unique properties from both sides, the graphene lateral spin valve can be useful in many applications. This dissertation mainly explores the use of graphene lateral spin valves for future computing and magnetic field sensing applications. This thesis firstly discusses the spin-circuit model, which is capable of simulating the dc, ac and transient behavior spintronic devices. Using the spin-circuit model, the scaling and energy consumption of all-spin logic devices is quantitatively studied. As one of the original proposals for spin-based computing, ASL utilizes lateral spin valves to process information in the spin domain. By using the physics-based spin-circuit model, the simulations suggest the effect of output-input isolation may be the fundamental challenges that prevent ASL from competing with CMOS in the scheme of conventional Boolean-computing. Next, this thesis explores the application of graphene lateral spin valves in non-Boolean computing and presents an implementation of spintronic Cellular Neural Networks (CNNs). In the graphene-based spintronic CNNs, weights are programmed as spin currents. Because of the tunable spin diffusion length in graphene, the weights can be controlled as local gate voltages, which can tune the weight values over a wide range. The simulation results show that the graphene-based spintronic CNNs have significantly improved scalability, particularly as the number and accuracy of synapses increases. In the last part of this thesis, the width scaling of graphene spin channels is experimentally studied, which is crucial for both the computing and magnetic field sensing applications. By using the graphene deposited by chemical vapor deposition (CVD) and a dedicated fabrication process, a large number of graphene lateral spin valves with consistent interface properties but different channel aspect ratios are fabricated on a single chip. The experimental results show that, as the channel width is scaled from 10 µm to 0.5 µm, the change in the nonlocal spin resistance matches the theory of contact-induced spin relaxation with the interface spin polarization, P, of 3 – 5 %, and spin diffusion length, λs, of 1.5 – 2.5 µm. Meanwhile, the spin-independent baseline resistance dramatically decreases due to the reduction in charge current spreading. However, we find that a remnant baseline remains due to the thermoelectric effects of graphene. By using the gate-voltage and bias-dependent analyses, we attribute the remnant baseline signal to the Joule-heating induced Seebeck voltage. These results suggest that in lateral spin valve design, to avoid any background signals, both the charge and thermal equilibrium conditions should be satisfied.