Solitons are waveforms that preserve their shape while propagating, as a result of a balance of dispersion and nonlinearity1,2. Soliton-based data transmission schemes were investigated in the 1980s and showed promise as a way of overcoming the limitations imposed by dispersion of optical fibres. However, these approaches were later abandoned in favour of wavelength-division multiplexing schemes, which are easier to implement and offer improved scalability to higher data rates. Here we show that solitons could make a comeback in optical communications, not as a competitor but as a key element of massively parallel wavelength-division multiplexing. Instead of encoding data on the soliton pulse train itself, we use continuous-wave tones of the associated frequency comb as carriers for communication. Dissipative Kerr solitons (DKSs)3,4 (solitons that rely on a double balance of parametric gain and cavity loss, as well as dispersion and nonlinearity) are generated as continuously circulating pulses in an integrated silicon nitride microresonator5 via four-photon interactions mediated by the Kerr nonlinearity, leading to low-noise, spectrally smooth, broadband optical frequency combs6. We use two interleaved DKS frequency combs to transmit a data stream of more than 50 terabits per second on 179 individual optical carriers that span the entire telecommunication C and L bands (centred around infrared telecommunication wavelengths of 1.55 micrometres). We also demonstrate coherent detection of a wavelength-division multiplexing data stream by using a pair of DKS frequency combs—one as a multi-wavelength light source at the transmitter and the other as the corresponding local oscillator at the receiver. This approach exploits the scalability of microresonator-based DKS frequency comb sources for massively parallel optical communications at both the transmitter and the receiver. Our results demonstrate the potential of these sources to replace the arrays of continuous-wave lasers that are currently used in high-speed communications. In combination with advanced spatial multiplexing schemes7,8 and highly integrated silicon photonic circuits9, DKS frequency combs could bring chip-scale petabit-per-second transceivers into reach.