Methods for measuring contemporary stress fields are reviewed with special attention given to problems with the existing hydraulic fracturing method. Regarding reopening pressure, we have no unique solutions for questions about the water pressure inside artificial fractures just before reopening. Furthermore, based on numerical simulations, several authors suggest that reopening pressure can be equal to shut-in pressure. Observation results also show that reopening pressure is almost equal to shut-in pressure at any depth throughout most of the world. If the latter suggestion is always true, the hydraulic fracturing method cannot determine the magnitude of maximum horizontal stress. Due to longstanding disputes, many different methods have been introduced over the past twenty years. Methods for measuring contemporary stress fields are based on basic knowledge of the physical properties of rocks and rock mechanics. To get answers to these questions, it is important to re-consider the basic principles of measurement methods.