Previous studies have noted the importance of electricity storage and hydrogen technologies for enabling large-scale variable renewable energy (VRE) deployment in long-term climate change mitigation scenarios. However, global studies, which typically use integrated assessment models, assume a fixed cost trajectory for storage and hydrogen technologies; thereby ignoring the sensitivity of VRE deployment and/or mitigation costs to uncertainties in future storage and hydrogen technology costs. Yet there is vast uncertainty in the future costs of these technologies, as reflected in the range of projected costs in the literature. This study uses the integrated assessment model, MESSAGE, to explore the implications of future storage and hydrogen technology costs for low-carbon energy transitions across the reported range of projected technology costs. Techno-economic representations of electricity storage and hydrogen technologies, including utility-scale batteries, pumped hydro storage (PHS), compressed air energy storage (CAES), and hydrogen electrolysis, are introduced to MESSAGE and scenarios are used to assess the sensitivity of long-term VRE deployment and mitigation costs across the range of projected technology costs. The results demonstrate that large-scale deployment of electricity storage technologies only occurs when techno-economic assumptions are optimistic. Although pessimistic storage and hydrogen costs reduce the deployment of these technologies, large VRE shares are supported in carbon-constrained futures by the deployment of other low-carbon flexible technologies, such as hydrogen combustion turbines and concentrating solar power with thermal storage. However, the cost of the required energy transition is larger. In the absence of carbon policy, pessimistic hydrogen and storage costs significantly decrease VRE deployment while increasing coal-based electricity generation. Thus, R&D investments that lower the costs of storage and hydrogen technologies are important for reducing emissions in the absence of climate policy and for reducing mitigation costs in the presence of climate policy.