We present extensive observations of the radio emission from the remnant of supernova (SN) 1987A made with the Australia Telescope Compact Array (ATCA), since the first detection of the remnant in 1990. The radio emission has evolved in time providing unique information on the interaction of the SN shock with the circumstellar medium. We particularly focus on the monitoring observations at 1.4, 2.4, 4.8, and 8.6 GHz, which have been made at intervals of 4-6 weeks. The flux density data show that the remnant brightness is now increasing exponentially, while the radio spectrum is flattening. The current spectral index value of –0.68 represents an 18 ± 3% increase over the last eight years. The exponential trend in the flux is also found in the ATCA imaging observations at 9 GHz, which have been made since 1992, approximately twice a year, as well as in the 843 MHz data set from the Molonglo Observatory Synthesis Telescope from 1987 to 2007 March. Comparisons with data at different wavelengths (X-ray, Hα) are made. The rich data set that has been assembled in the last 22 years forms a basis for a better understanding of the evolution of the supernova remnant.