Sparse code multiple access (SCMA) is a class of non-orthogonal multiple access that is proposed to support uplink machine-type communication services. In this thesis, we investigate the design of SCMA systems from two main aspects: multidimensional constellations (MdCs) and efficient detection schemes. In an SCMA system, designing MdCs plays an important role in the system performance. Since the behavior of multidimensional constellations highly depends on the type of the channel, it is crucial to employ a constellation that is suitable for a certain application. In the fifirst part of this thesis, we highlight and review the key performance indicators (KPIs) of MdCs that should be considered in their design process for various channel scenarios. We also provide a survey on the known MdCs in the context of SCMA systems with their design criteria. The performance of some of those constellations are evaluated for uncoded and LTE turbo-coded SCMA systems under different channel conditions through extensive simulations. We then investigate the effect of the 5G low density parity check (LDPC) codes on determining KPIs in designing MdCs under various channel scenarios. Since the optimal maximum likelihood (ML) receiver for SCMA is too complex in most applications, one highly popular detection technique is the message passing algorithm (MPA), which exploits the sparsity structure of SCMA. MPA is a near-optimal technique, where its performance improves with increasing the signal-to-noise-ratio (SNR) and the number of iterations. We design novel SCMA SNR-adaptive MdCs which result in substantial performance gains (as much as 2 dB) in comparison to the best known SCMA MdCs in the literature, especially in low-to-medium SNR regions when the number of MPA iterations has to be low, and in the presence of 5G-compliant LDPC codes. Sphere decoding (SD) based detection schemes for SCMA have recently received attention due to their promising features. However, the existing SD-based schemes can only be applied to systems with constellations that possess a certain structure. In the second part of the thesis, we propose an SD-based detection scheme, namely improved SD (ISD), for SCMA that achieves the optimal ML detector for any arbitrary regular or irregular constellations.