Augmented reality for laparoscopic liver resection is a visualisation mode that allows a surgeon to localise tumours and vessels embedded within the liver by projecting them on top of a laparoscopic image. Preoperative 3D models extracted from Computed Tomography (CT) or Magnetic Resonance (MR) imaging data are registered to the intraoperative laparoscopic images during this process. Regarding 3D-2D fusion, most algorithms use anatomical landmarks to guide registration, such as the liver's inferior ridge, the falciform ligament, and the occluding contours. These are usually marked by hand in both the laparoscopic image and the 3D model, which is time-consuming and prone to error. Therefore, there is a need to automate this process so that augmented reality can be used effectively in the operating room. We present the Preoperative-to-Intraoperative Laparoscopic Fusion challenge (P2ILF), held during the Medical Image Computing and Computer Assisted Intervention (MICCAI 2022) conference, which investigates the possibilities of detecting these landmarks automatically and using them in registration. The challenge was divided into two tasks: (1) A 2D and 3D landmark segmentation task and (2) a 3D-2D registration task. The teams were provided with training data consisting of 167 laparoscopic images and 9 preoperative 3D models from 9 patients, with the corresponding 2D and 3D landmark annotations. A total of 6 teams from 4 countries participated in the challenge, whose results were assessed for each task independently. All the teams proposed deep learning-based methods for the 2D and 3D landmark segmentation tasks and differentiable rendering-based methods for the registration task. The proposed methods were evaluated on 16 test images and 2 preoperative 3D models from 2 patients. In Task 1, the teams were able to segment most of the 2D landmarks, while the 3D landmarks showed to be more challenging to segment. In Task 2, only one team obtained acceptable qualitative and quantitative registration results. Based on the experimental outcomes, we propose three key hypotheses that determine current limitations and future directions for research in this domain.