Carbon Capture and Sequestration (CCS), which combines capture of CO2 from large stationary sources with geological storage, has emerged as an attractive option for emissions reduction. Hydrogen underground storage (HUS) is viewed as an effective strategy for storing large volumes of surplus electrical energy from renewable sources. The objective of this paper is to discuss the opportunities and challenges for adapting petroleum reservoir engineering techniques for the subsurface aspects of CCS and HUS projects based on a critical review of field projects and conceptual studies. Areas of focus include: (a) storage resource estimation, injectivity analysis from field data, dynamic reservoir modeling, and coupled flow and geomechanics for CCS, and (b) well deliverability, dynamics of fluid withdrawal and reactive transdport of hydrogen in-situ for HUS projects. Specifically, our goal is to discuss how traditional workflows for oil and gas applications have been (or could be) modified for CCS projects in deep saline formations and HUS projects in salt caverns or aquifers. We also identify specific areas where reservoir engineering practitioners can add value in CCS and HUS related reservoir analysis and modeling.