Recent discoveries of phosphorylation gradients and microdomains with different protein activities have revolutionized our perception of information transfer within single cells. The different spatial localization of opposing reactions in protein-modification cycles has been shown to bring about heterogeneous stationary patterns and travelling waves of protein activities. We review spatial patterns and modes of signal transfer through phosphorylation/dephosphorylation and GDP/GTP exchange cycles and cascades. We show how switches between low-activity and high-activity states in a bistable activation-deactivation cycle can initiate the propagation of travelling protein-modification waves in the cytoplasm. Typically, an activation wave is initiated at the plasma membrane and propagates through the cytoplasm until it reaches the nucleus. An increase in deactivator activity is followed by the initiation of an inactivation wave that moves in the reverse direction from the nucleus. We show that the ratio of opposing enzyme rates is a key parameter that controls both the spread of activation through cascades and travelling waves.