Non-Collinear High-Harmonic Generation and Spectroscopy: From Basic Principles to Emerging Applications

High-harmonic generation (HHG), a cornerstone of attosecond science, has evolved into a powerful all-optical spectroscopic tool. However, conventional collinear multicolor schemes face intrinsic limitations, notably intense single-beam backgrounds that obscure weak signals and difficulties in disentangling multidimensional information. This review highlights the transformative potential of non-collinear highharmonic generation and spectroscopy (NC-HHGS). By crossing driving beams at a finite angle, this geometry creates a transient optical grating that inherently resolves photon energy and momentum. This elegant approach enables background-free detection, provides built-in momentum resolution via the emission angle, and grants access to multi-dimensional spectroscopy by simultaneously mapping temporal, spectral, and momentum degrees of freedom. Following a comprehensive overview of the underlying theoretical and experimental frameworks, we evaluate the use of non-collinear geometries for spatial control and field tailoring, specifically regarding emission isolation, field shaping, and efficiency enhancement. We further examine their application in characterizing material dynamics, focusing on ultrafast electronic, excitonic, and structural transitions in bulk solids. Finally, we discuss remaining challenges and future opportunities for establishing NC-HHGS as a standard table-top methodology for attosecond science.