We report on new approaches to picosecond fluorescence spectroscopy, using commercial silicon avalanche photodiodes (APD's) as opto-electronic cross-correlators. By integrating lock-in techniques, fluorescence radiation can be detected with 0.001 photons per pulse sensitivity. In our method, the internal gain of the APD is modulated in synchronism with a syncpumped cw dye laser. Using pulsed gain-modulation, time-domain measurements with an apparatus response FWHM of 150 ps can be accomplished. In a second mode, sinusoidal gain-modulation is employed, enabling frequency-domain measurements up to about 3000 MHz at multiples of the laser pulse repetition frequency. This mode also allows high-resolution lifetime-selective detection and fluorescence lifetime direct indication.