The experimental demonstration of photon antibunching was the first direct verification of nonclassical light through normal- and time-ordered intensity correlation measurements. Until now, nonclassical light is often studied only for a single time. Here, a universal approach is provided for the characterization of general space- and time-dependent quantum properties of light. For their study, homodyne intensity correlation measurements have been proposed already in 1991, for the detection of squeezing in resonance fluorescence. Almost a quarter century later, this experiment has been performed. Homodyne cross correlation measurements have been conducted to demonstrate anomalous quantum correlations of squeezed light. Also balanced and unbalanced homodyne correlation techniques have been developed. Another established method of quantum correlation measurements is based on multiplexing click counting devices. We consider the detection of the quantum properties of a fully dephased two-mode squeezed vacuum. Phase-space functions have been determined by homodyne click counting. Interestingly, the incomplete detection by click detectors yields better insight in the quantum effects than the measurement of the full counting statistics.