This thesis describes our studies of non-equilibrium spin accumulation in ferromagnet/n-GaAs heterostructures. This work naturally separates into two main topics: the first is the study of the non-equilibrium electron spin accumulation which is generated electrically by passing a current across the ferromagnet/GaAs interface; the second is the study of non-equilibrium nuclear spin accumulation which is dynamically generated via flip-flop interactions with the spin-polarized electrons. Chapter 1 covers the theoretical framework which we use to electrically study the injection and detection of electron spins into GaAs. This framework includes two relevant mechanisms for injection and detection of spins, which provide different results depending on the nature of the tunneling current across the ferromagnet/GaAs interface. This section also outlines the basic electrical measurements used to study spins in GaAs, and outlines the results determined from studies of Fe/GaAs heterostructures. In Chapter 2 we apply this knowledge to a new class of ferromagnetic materials. We present electrical spin transport measurement of Co2FeMnSi/n-GaAs heterostructures. Co2FeMnSi are alloys of Heusler ferromagnets that have been predicted by band structure calculations to be highly spin-polarized at the Fermi level, making them ideal for spin injection and detection. Using a biased detector measurement scheme, we demonstrate mV spin-valve signals at low temperature, the largest measured in III/V semiconductor systems. We show that the spin accumulation in the GaAs channel changes sign as a function of the Fe concentration, in agreement with theory. In addition we show that the measured spin accumulation is an order of magnitude larger than for Fe based devices, further supporting the idea that these ferromagnets are highly spin-polarized.Chapter 3 focuses on the experimental evidence and theory of a non-equilibrium nuclear spin polarization. The nuclear spin polarization is generated dynamically by hyperfine interactions with the spin-polarized electrons in the channel. We show that a phenomenological description of the hyperfine interaction in terms of effective magnetic fields can reproduce our measurements. In Chapter 4 we study the hyperfine interaction between spin-polarized electrons and nuclei more carefully. We show by a nuclear magnetic resonance experiment that spin-polarized nuclei are localized near donor sites, the spin-polarized nuclei are not spatially homogeneous as often assumed. Further we argue that the fraction of these donor sites which contribute to polarizing the nuclei can be estimated by modeling our resistivity data by the dual conduction of electrons through the impurity and conduction bands. Finally we demonstrate the Knight shift of the NMR frequency as a function of the electron spin accumulation. Using these results, it is possible to determine the electron spin accumulation without microscopic knowledge of the ferromagnet/GaAs interface that was used to generate it.