In Zdziarski et al. (2007a), we have performed a comprehensive analysis of the superorbital modulation in the ultracompact X-ray source 4U 1820-303, consisting of a white dwarf accreting onto a neutron star Based on RXTE data, we measured the fractional amplitude of the source superorbital variability (with a ∼ 170-d quasi-period) in the folded and averaged light curves, and found it to be by a factor of ∼2. As proposed before, that variability can be explained by oscillations of the binary eccentricity. in that work, we presented detailed calculations of the eccentricitydependent flow through the inner Lagrangian point, and found a maximum of the eccentricity of ∼ 0.004 is sufficient to explain the observed fractional amplitude. We then studied hierarchical triple models yielding the required quasi-periodic eccentricity oscillations through the Kozai process. We found the resulting theoretical light curves to match well the observed ones. We constrained the ratio of the semimajor axes of the outer and inner systems, the component masses, and the inclination angle between the inner and outer orbits. Last but not least, we discovered a remarkable and puzzling synchronization between the observed period of the superorbital variability (equal to the period of the eccentricity oscillations in our model) and the period of the general-relativistic periastron precession of the binary. in Zdziarski et al. (2007b), we have reported the discovery, using RXTE data, of a dependence of the X-ray orbital modulation depth on the X-ray spectral state. This state (measured by the position on the colour-colour diagram) is tightly coupled to the accretion rate, which, in turn, is coupled to the phase of the ∼ 170-d superorbital cycle. The modulation depth is much stronger in the highluminosity, so-called banana, state than in the low-luminosity, island, state. We found the X-ray modulation was independent of energy, which ruled out bound-free X-ray absorption in an optically thin medium as the cause of the modulation. We also found a significant dependence of the offset phase of the orbital modulation on the spectral state, which favoured a model with the modulation caused by scattering in hot gas around a bulge at the disc edge, and with the size and the position of the bulge varying with the accretion rate. Estimates of the source inclination appear to rule out a model in which the bulge itself occults a part of an accretion disc corona. We calculated the average flux of this source over the course of its superorbital variability (which has the period of ∼ 170- d), and found it to be fully compatible with the model of accretion due to the angular momentum loss via emission of gravitational radiation. Also, we compared the dates of all X-ray bursts observed from this source by BeppoSAX and RXTE with the RXTE light curve, and found all of them to coincide with deep minima of the flux, confirming previous results based on smaller samples.