We present here a review of the most significant recent achievements in the field of HAXPES (HArd X-ray PhotoElectron Spectroscopy) on isolated atoms and molecules, and related spectroscopies. The possibility of conducting hard x-ray photoexcitation and photoionization experiments under state-of-the art conditions in terms of photon and electron kinetic energy resolution has become available only in the last few years. HAXPES has then produced structural and dynamical information at the level of detail already reached in the VUV and soft-x-ray ranges. The much improved experimental conditions have allowed extending to the hard x-ray range some methods well established in soft x-ray spectroscopies. Investigations of electron and nuclear dynamics in the femtosecond (fs, 10-15 sec) and even attosecond (as, 10-18 sec) regime have become feasible. Complex relaxation phenomena following deep-core ionization can now be enlightened in great detail. Other phenomena like e.g. recoil-induced effects are much more important in fast photoelectron emission, which can be induced by hard x-rays. Furthermore, a new kind of ionic states with double core holes can be observed by x-ray single-photon absorption. Future perspectives are also discussed. Contents: 1. Introduction 2. Background 2.1 Auger resonant Raman 2.2 Core-hole-clock 2.3 Effective scattering time 2.4 Post-collision interaction 2.5 Cascade Auger decay 2.6 Double-core-hole studies 3. Instrumentation 3.1 Beam lines 3.2 Spectrometers 4. Recent results 4.1 RIXS: reaching the attosecond timescale 4.2 Double-core-hole studies by single-channel photoemission 4.3 Direct derivation of potential energy surfaces 4.4 Ultrafast photodissociation in the Auger cascade following deep-core excitation 4.5 Recoil due to the photoelectron's momentum 4.6 Exotic Auger decay pathways 4.7 Novel interference phenomena 4.8 Electron-recapture and post-collision interaction effects 4.9 Disentangling complex decay patterns after deep-core-hole ionization 4.10 Core-hole localization/delocalization 5. Perspectives 6. Conclusion 7. Acknowledgments 8. Literature references