About 150 weakly magnetic neutron stars are known to accrete matter from low-mass stars in neutron star low-mass X-ray binaries (NS-LMXBs). Accretion in these systems is not steady and as a consequence luminosity and spectral shape change on timescales from milliseconds to months. Energy spectrum and rapid variability vary in a correlated way, which allows to classify NS-LMXBs into two main groups: Z sources and atoll sources. Both Z and atoll sources exhibit different accretion states, as witnessed by their changing spectral and variability properties, which reflect different configurations of the accretion flow around the neutron star. While there are various clues that the relation between accretion state and X-ray luminosity is not simple, lack of systematic study of this issue has prevented firm conclussions up to now. We present a systematic study of accretion states and state transitions in a sample of atoll sources in relation to their luminosity. Using data from both PCA and HEXTE onboard the RXTE we obtain reliable estimates of the time dependent bolometric luminosity of the sources. We also devised a method to efficiently characterize their timing/variability state. One of the results of applying these methods is that in 4U 1608-522 the transitions between low-luminosity hard-spectrum (island) states and high-luminosity soft-spectrum (banana) states happen around two distinct luminosities. Contrary to what studies suggest to be the case in black hole X-ray binaries, the hard-to-soft transition in atoll sources does not always happen at a higher luminosity than the soft-to-hard transition. We also investigate the complex relation between variability frequencies and luminosity.