Data exchange, namely bidirectional information swapping, provides enhanced flexibility compared to the unidirectional information transfer. To fulfill the rapid development of high-speed large-capacity optical communications with emerging multiplexing/demultiplexing techniques and advanced modulation formats, a laudable goal would be to achieve data exchange in different degrees of freedom (wavelength, time, polarization), for different modulation formats (OOK, DPSK, DQPSK, pol-muxed), and at different granularities (entire data, groups of bits, tributary channels). Optical nonlinearities are potentially suitable candidates to enable data exchange in the wavelength, time, and polarization domains. In this paper, we will review our recent works towards robust data exchange by exploiting miscellaneous optical nonlinearities, including the use of cSFG/DFG in a PPLN waveguide for time- (groups of bits) and channel-selective data exchange and tributary channel exchange between two WDM+OTDM signals, nondegenerate FWM in an HNLF for phase-transparent data exchange (DPSK, DQPSK), bidirectional degenerate FWM in an HNLF for multi-channel data exchange, and Kerr-induced nonlinear polarization rotation in an HNLF for tributary channel exchange of a pol-muxed DPSK OTDM signal. The demonstrated data exchanges in different degrees of freedom, for different modulation formats, and at different granularities, open the door for alternative approaches to achieve superior network performance.