Context. The advent of deep, multi-wavelength surveys, together with the availability of extensive numerical simulations, now allow us for the systematic search and study of (proto)clusters and their surrounding environment as a function of redshift.Aims. We aim to define the environment and to identify overdensities in the VANDELS Chandra Deep Field-South (CDFS) and UKIDSS Ultra Deep Survey (UDS) fields. We want to investigate whether we can use Ly alpha emission to obtain additional information of the environment properties and whether Ly alpha emitters show different characteristics as a function of their environment.Methods. We estimated local densities using a three-dimensional algorithm which works in the RA-dec-redshift space. We took advantage of the physical parameters of all the sources in the VANDELS fields to study their properties as a function of environment. In particular, we focused on the rest-frame U-V color to evaluate the stage of evolution of the galaxies located in the overdensities and in the field. Then we selected a sample of 131 Ly alpha -emitting galaxies (EW(Ly alpha) > 0 angstrom), unbiased with respect to environmental density, from the first two seasons of the VANDELS survey to study their location with respect to the over- or under-dense environment and infer whether they are useful tracers of overdense regions.Results. We identify 13 (proto)cluster candidates in the CDFS and nine in the UDS at 2< z< 4, based on photometric and spectroscopic redshifts from VANDELS and from all the available literature. No significant difference is observed in the rest-frame U-V color between field and galaxies located within the identified overdensities, but the star-forming galaxies in overdense regions tend to be more massive and to have low specific SFRs than in the field. We study the distribution of the VANDELS Ly alpha emitters (LAEVs) and we find that Ly alpha emitters lie preferentially outside of overdense regions as the majority of the galaxies with spectroscopic redshifts from VANDELS. The LAEVs in overdense regions tend to have low Ly alpha equivalent widths and low specific SFRs, and they also tend to be more massive than the LAEVs in the field. Their stacked Ly alpha profile shows a dominant red peak and a hint of a blue peak. There is evidence that their Ly alpha emission is more extended and offset with respect to the UV continuum.Conclusions. LAEVs are likely to be influenced by the environment. In fact, our results favour a scenario that implies outflows of low expansion velocities and high HI column densities for galaxies in overdense regions. An outflow with low expansion velocity could be related to the way galaxies are forming stars in overdense regions; the high HI column density can be a consequence of the gravitational potential of the overdensity. Therefore, Ly alpha -emitting galaxies can provide useful insights on the environment in which they reside.