X-ray binaries are formed by a compact object (either a stellar-mass black hole or a neutron star) and a donor star, which transfers mass onto the former via an accretion disc. They are usually discovered thanks to their bright X-ray radiation, but observations at other wavelengths are mandatory to fully understand and characterise their extreme phenomenology. In this thesis, we present a multiwavelength observational study of five low mass X-ray binaries (LMXBs); a subclass defined by their late spectral type companion stars (< 1 Msun). The selected binaries contain both accreting neutron stars and black holes.  

We first study two recently discovered transient systems whose fundamental parameters are still under debate.

The first is MAXI J1957+032, a recently discovered X-ray transient which has been detected in outburst 4 times in about 16 months, each outburst with equally short duration (< 5 days). These frequent and short outbursts (when compared with other transients), combined with the featureless spectrum that we obtained during the September 2016 event, suggest this may be a new short orbital period LMXB. In this thesis, we report on some of its main properties, such as the distance and luminosity. However, the nature of the compact star remains unknown.

The second system, Swift J1357.2-0933, was discovered during an outburst in 2011 and classified as a LMXB harbouring a black hole. We obtained optical spectroscopy with GTC during quiescence, when the disc contribution to the optical flux is at its minimum. However, we did not find any trace of the donor star absorption features. Our spectroscopic analysis set new constraints on the non-stellar contribution to the optical flux, which allows us to estimate the distance and the height of the system above the Galactic plane. We also present a restrictive limit to the black hole mass (> 9.3 Msun). Therefore, Swift J1357.2-0933 is one of the most massive stellar-mass black holes ever found in our Galaxy, as well as a member of the new population of the thick disc, located >1 kpc outside the Galactic plane.

Subsequently, we analysed two canonical binaries that harbour neutron stars with the aim to study their donor stars, which have never been detected before.

Scorpius X-1 is the canonical persistent neutron-star LMXB. Despite it was discovered at the dawn of X-ray astronomy (more than 50 years ago), its persistent nature has prevented a proper dynamical study as it requires the detection of the donor star (only possible during the quiescence phase). We obtained near-infrared spectroscopy and performed a Monte Carlo analysis that allows us to set tighter constraints on the masses of this prototypical system.

Aquila X-1 is also a canonical neutron-star LMXB, but in this case of the subtype of transient systems. It exhibits recurrent outbursts every two years, and has been exhaustively studied since its discovery more than 40 years ago. In spite of its accessible quiescent brightness (both in the optical and near-infrared), its dynamical study has been hampered so far by the presence of a brighter nearby (0.4 arcsec away) field star. Combining the integral field spectrograph SINFONI attached to the VLT telescope with its adaptive optics module, we singled out Aquila X-1 and obtained phase-resolved spectra. This allowed us to detect, for the first time, its donor star absorption features, as well as to measure its radial velocity curve. We set new constraints on the distance to the system, as well as the orbital inclination which discards high neutron star masses.

To complete this sample, we also present the results of the most extensive optical spectroscopic campaign ever performed (to our knowledge) on an outburst of a transient X-ray binary system. V404 Cygni is a LMXB which contains a black hole. The system exhibits outbursts every 25 years. Its dynamical parameters have been measured and refined over the course of the last decades. Our new large database of 651 spectra covering the entire June 2015 outburst allows us to touch up the \textit{painting} of this transient. In particular, we detect continuous mass outflows from the accretion disc in the form of a cold wind (P-Cygni profiles), as well as an expanding nebula. Our study suggests that the outflow plays a major role in regulating the outburst evolution.

Through the analysis of these five low mass X-ray binaries, this thesis provides new results on both their fundamental parameters and the relevant accretion-related physical processes at work. It also presents an extensive collection of the observational techniques employed along the different stages of the research process, that is, from the rough sketch of the system depicted by the initial detection in the X-rays, to a more detailed painting that detailed multiwavelength follow-up (both in outburst and quiescence) enables to elaborate.