Transmission spectroscopy provides us with information on the atmospheric properties at the limb, which is often intuitively assumed to be a narrow annulus around the planet. Consequently, studies have focused on the effect of atmospheric horizontal heterogeneities along the limb. Here we demonstrate that the region probed in transmission – the limb – actually extends significantly towards the day and night sides of the planet. We show that the strong day–night thermal and compositional gradients expected on synchronous exoplanets create sufficient heterogeneities across the limb that result in important systematic effects on the spectrum and bias its interpretation. To quantify these effects, we developed a 3D radiative-transfer model able to generate transmission spectra of atmospheres based on 3D atmospheric structures. We first apply this tool to a simulation of the atmosphere of GJ 1214 b to produce synthetic JWST observations and show that producing a spectrum using only atmospheric columns at the terminator results in errors greater than expected noise. This demonstrates the necessity for a real 3D approach to model data for such precise observatories. Secondly, we investigate how day–night temperature gradients cause a systematic bias in retrieval analysis performed with 1D forward models. For that purpose we synthesise a large set of forward spectra for prototypical HD 209458 b- and GJ 1214 b-type planets varying the temperatures of the day and night sides as well as the width of the transition region. We then perform typical retrieval analyses and compare the retrieved parameters to the ground truth of the input model. This study reveals systematic biases on the retrieved temperature (found to be higher than the terminator temperature) and abundances. This is due to the fact that the hotter dayside is more extended vertically and screens the nightside – a result of the non-linear properties of atmospheric transmission. These biases will be difficult to detect as the 1D profiles used in the retrieval procedure are found to provide an excellent match to the observed spectra based on standard fitting criteria. This must be kept in mind when interpreting current and future data.