Sparse code multiple access (SCMA) is a class of non-orthogonal multiple access (NOMA) that is proposed to support uplink machine-type communication services. In an SCMA system, designing multidimensional constellation plays an important role in the performance of the system. Since the behaviour 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 this paper, we first highlight and review the key performance indicators (KPIs) of multidimensional constellations that should be considered in their design process for various channel scenarios. We then provide a survey on the known multidimensional constellations in the context of SCMA systems with their design criteria. The performance of some of those constellations are evaluated for uncoded, high-rate, and low-rate LTE turbo-coded SCMA systems under different channel conditions through extensive simulations. All turbo-coded comparisons are performed for bit-interleaved coded modulation, with a concatenated detection and decoding scheme. Simulation results confirm that multidimensional constellations that satisfy KPIs of a certain channel scenario outperform others. Moreover, the bit error rate performance of uncoded systems, and the performance of the coded systems are coupled to their bit-labeling. The performance of the systems also remarkably depends on the behavior of the multi-user detector at different signal-to-noise ratio regions.