Oil and gas reservoirs in volcanic rocks are a particular type of unconventional reservoir and present unique challenges for exploration and production engineers. To help the oil industry understand volcanic reservoirs and solutions to complex development problems, we reviewed their key engineering technologies as well as their geological characteristics. The distinctive geological characteristics of volcanic hydrocarbon reservoirs are strong heterogeneity, low porosity and permeability, complex fracture systems, etc. The volcanic reservoir rock types in order of hydrocarbon abundance are basalt (38.5%), andesite (15.9%), volcaniclastic (12.1%), and rhyolite (11.5%). The porosity ranges from 0.1 to 70%, and permeability ranges from 0.0007 to 762 md. In some commercially developed volcanic reservoirs of China, the average porosity is 7.7–13%; the average permeability is 0.41–3.4 md. Engineers have applied a variety of adapted technologies to produce volcanic reservoir economically. Horizontal wells can increase production and reserves by 4–6 times those of vertical wells, and longer wells are preferred. Specialized hydraulic fracturing techniques are suggested, including small or mixed proppant size, second HF treatment after proppant slugging, high-viscosity frac fluid with high-temperature resistance, special fluid loss reducer, high pump pressure, Extreme Overbalance Perforating, limited-entry fracturing, matrix acidizing, etc. Water control measures include producing below critical rates, partial perforation or penetration, controlling hydraulic fracture height, using horizontal wells, implementing complete cementing job, etc. Well productivity evaluation should be conducted to understand well performance and appropriately allocate production rates among wells, using the modified AOF method and other productivity prediction models considering breakdown fracture gradient, gas slippage effect, non-Darcy effect, etc. Well sites need to be selected based on recognizing profitable lithologies, lithofacies, high porosity and permeability, relatively developed fracture systems, thick net pay zones, etc. The critical questions for the industry are how to enhance volcanic reservoir recovery with more efficient and economic hydraulic fracturing and water control techniques. This is one of the first papers systematically summarizing the engineering technologies and unique solutions to develop volcanic reservoirs. Further and more complete reviews can be carried out in the future, and more novel and effective techniques can be explored and tested in the field.