Abstract: This report summarises some of the activities of the HiggsTools initial training network working group in the period 2015-2017. The main goal of this working group was to produce a document discussing various aspects of state-of-the-art Higgs physics at the large hadron collider (LHC) in a pedagogic manner The first part of the report is devoted to a description of phenomenological searches for new physics (NP) at the LHC. All of the available studies of the couplings of the new resonance discovered in 2012 by the ATLAS and CMS experiments (Aad et al (ATLAS Collaboration) 2012 Phys. Lett. B 716 1-29; Chatrchyan et al (CMS Collaboration) 2012 Phys. Lett. B 716 30-61) conclude that it is compatible with the Higgs boson of the standard model (SM) within present precision. So far the LHC experiments have given no direct evidence for any physical phenomena that cannot be described by the SM. As the experimental measurements become more and more precise, there is a pressing need for a consistent framework in which deviations from the SM predictions can be computed precisely. Such a framework should be applicable to measurements in all sectors of particle physics, not only LHC Higgs measurements but also electroweak precision data, etc. We critically review the use of the k-framework, fiducial and simplified template cross sections, effective field theories, pseudoobservables and phenomenological Lagrangians. Some of the concepts presented here are well known and were used already at the time of the large electron-positron collider (LEP) experiment. However, after years of theoretical and experimental development, these techniques have been refined, and we describe new tools that have been introduced in order to improve the comparison between theory and experimental data. In the second part of the report, we propose Phi(eta)* as a new and complementary observable for studying Higgs boson production at large transverse momentum in the case where the Higgs boson decays to two photons. The Phi(eta)* variable depends on measurements of the angular directions and rapidities of the two Higgs decay products rather than the energies, and exploits the information provided by the calorimeter in the detector. We show that, even without tracking information, the experimental resolution for Phi(eta)* is better than that of the transverse momentum of the photon pair, particularly at low transverse momentum. We make a detailed study of the phenomenology of the Phi(eta)* variable, contrasting the behaviour with the Higgs transverse momentum distribution using a variety of theoretical tools including event generators and fixed order perturbative computations. We consider the theoretical uncertainties associated with both p TH and Phi(eta)* distributions. Unlike the transverse momentum distribution, the Phi(eta)* distribution is well predicted using the Higgs effective field theory in which the top quark is integrated out-even at large values of Phi(eta)*-thereby making this a better observable for extracting the parameters of the Higgs interaction. In contrast, the potential of the Phi(eta)* distribution as a probe of NP is rather limited, since although the overall rate is affected by the presence of additional heavy fields, the shape of the Phi(eta)* distribution is relatively insensitive to heavy particle thresholds.