Intracellular calcium waves refer to the coordinated propagation of increased free calcium ion (Ca) concentration in the cytoplasm. Ca is one of the major intracellular second messengers which coordinates many cells function including gene transcription, division, and cell apoptosis. The spread of the ions in the cytoplasm is not the same in all cell types. Experiments indicate the strength of the stimuli, the site of the first Ca entry and the localization of the organelles influence the Ca propagation and may lead to functional compartmentalization. Polarized cells with complex anatomy already have anatomical subparts (like processes) which elevate the probability of the functional separation between the cell parts. Cells are stimulated at special parts where the receptors/channels are located. Ca enters the cell via ligand or voltage gated calcium channels, connexin channels from the neighboring cells or with the activation of G-protein coupled receptors which activate Ca release from the cytosolic Ca stores. The emptying stores may activate store-operated Ca channels, too. These local signals could globalize and elevate free Ca concentration in the cells. Smaller, more compact cells form a uniformly activated cell, however, in polarized cells this cannot happen in each time, leads to spatiotemporally different subpart activation. In this review, we discuss the main mechanisms of the cells which involved in Ca signaling and the possible methods how a single event (a Ca spike) can form slow intracellular Ca wave and globalized signal. Intracellular Ca waves were found in multiple cell types starting with simple egg cells. Here, we bring examples to anatomically more complex polarized cells with processes, but without excitability: the radial glia, astrocytes, Müller glia and osteocytes as a cell does not connect strongly to sensory-neural structures.