IRBis is an image reconstruction method for optical/infrared long-baseline interferometry. IRBis can reconstruct images from (a) measured visibilities and closure phases, or from (b) measured complex visibilities (i.e. the Fourier phases and visibilities). The applied optimization routine ASA CG is based on conjugate gradients. The method allows the user to implement different regularizers, as for example, maximum entropy, smoothness, total variation, etc., and apply residual ratios as an additional metric for goodness-of-fit. In addition, IRBis allows the user to change the following reconstruction parameters: (a) FOV of the area to be reconstructed, (b) the size of the pixel-grid used, (c) size of a binary mask in image space allowing reconstructed intensities < 0 within the binary mask only, (d) the strength of the regularization, etc. The two main reconstruction parameters are the size of the binary mask in image space (c) and the strength of the regularization (d). Several values of these two parameters are tested within the algorithm. The quality of the different reconstructions obtained is roughly estimated by evaluation of the differences between the measured data and the reconstructed image (using the reduced χ2 values and the residual ratios). The best-quality reconstruction and a few reconstructions sorted according to their quality are provided to the user as resulting reconstructions. We describe the theory of IRBis and will present several applications to simulated interferometric data and data of real astronomical objects: (a) We have investigated image reconstruction experiments of MATISSE target candidates by computer simulations. We have modeled gaps in a disk of a young stellar object and have simulated interferometric data (squared visibilities and closure phases) with a signal-to-noise ratio as expected for MATISSE observations. We have performed image reconstruction experiments with this model for different flux levels of the target and different amount of observing time, that is, with different uv coverages. As expected, the quality of the reconstructions clearly depends on the flux of the source and the completeness of the uv coverage. (b) We also discuss reconstructions of the Luminous Blue Variable η Carinae obtained from AMBER observations in the high spectral resolution mode in the K band. The images were reconstruction (1) using the closure phases and (2) using the absolute phases derived from the measured wavelength-differential phases and the closure phase reconstruction in the continuum.