In this paper we describe our recent results on the study of avalanche photodiodes for detection of scintillation of liquid xenon, namely measurements of very low intensity light pulses and the photodiode excess noise as a function of temperature. Some other aspects relevant to the use of liquid xenon scintillation for particle detection are also addressed. In particular, we refer our measurements of the refraction index and attenuation length of the liquid for the VUV light emitted by xenon, which were found to be 1.69±0.02 and 36.4±1.8 cm, respectively.