Ca2+ signalling is perhaps the most universal and versatile mechanism regulating a wide range of cellular processes. Because of the many different calcium‐binding proteins distributed throughout cells, signalling precision requires localized rises in the cytosolic Ca2+ concentration. In electrically non‐excitable cells, for example epithelial cells, this is achieved by primary release of Ca2+ from the endoplasmic reticulum via Ca2+ release channels placed close to the physiological target. Because any rise in the cytosolic Ca2+ concentration activates Ca2+ extrusion, and in order for cells not to run out of Ca2+, there is a need for compensatory Ca2+ uptake from the extracellular fluid. This Ca2+ uptake occurs through a process known as store‐operated Ca2+ entry. Ideally Ca2+ entering the cell should not diffuse to the target site through the cytosol, as this would potentially activate undesirable processes. Ca2+ tunnelling through the lumen of the endoplasmic reticulum is a mechanism for delivering Ca2+ entering via store‐operated Ca2+ channels to specific target sites, and this process has been described in considerable detail in pancreatic acinar cells and oocytes. Here we review the most important evidence and present a generalized concept.