Constellation modulation (CM) is introduced as a new degree of freedom to increase the spectral efficiency and to further approach the Shannon limit. Constellation modulation is the art of encoding information not only in the symbols within a constellation but also by encoding information by selecting a constellation from a set of constellations that are switched from time to time. The set of constellations is not limited to sets of partitions from a given constellation but can e.g., be obtained from an existing constellation by applying geometrical transformations such as rotations, translations, scaling, or even more abstract transformations. The architecture of the transmitter and the receiver allows for constellation modulation to be used on top of existing modulations with little penalties on the bit-error ratio (BER) or on the required signal-to-noise ratio (SNR). The spectral bandwidth used by this modulation scheme is identical to the original modulation. Simulations demonstrate a particular advantage of the scheme for low SNR situations. So, for instance, it is demonstrated by simulation that a spectral efficiency increases by up to 33% and 20% can be obtained at a BER of 10-3 and 2×10-2 for a regular BPSK modulation format, respectively. Applying constellation modulation, we derive a most power efficient 4D-CM-BPSK modulation format that provides a spectral efficiency of 0.7 bit/s/Hz for an SNR of 0.2 dB at a BER of 2 × 10-2.