L-asparaginase is a critical part of the treatment of acute lymphoblastic leukaemia in children and adolescents, and has contributed to the improvement in patient outcomes over the last 40 years. The main products used in clinical treatment are L-asparaginase enzymes derived from Escherichia coli and Erwinia chrysanthemi. However, a very active area of research is the identification and characterisation of potential new L-asparaginase therapeutics, from existing or novel prokaryotic and eukaryotic sources, including mutations to improve function. In this review, we discuss the critical factors necessary to adequately characterise novel L-asparaginase therapeutic products, including enzyme kinetic parameters, glutaminase activity, and toxicity. One critical consideration is to ensure that the substrate affinity of novel enzymes, as measured by the Michaelis constant K, is sufficiently low to enable efficient reaction rates in human clinical use. The activity of L-asparaginases towards glutamine as a substrate is discussed and reviewed in detail, as there is much debate in the scientific literature about the importance of this feature for therapeutic enzymes. The recent research in the area is reviewed, including identification of new sources of the enzyme, modulating glutaminase activity, and improving the thermal stability and immunogenic response. New research in the area may benefit from these considerations, to enable the next generation of therapeutic product design. Critical to future work in this area is a complete characterisation of novel enzymes with respect to performance for both L-asparagine and L-glutamine as substrates.