Abstract: Earthquakes represent dynamic processes in rocky planets where accumulated stress leads to sudden rupture, block movement, and energy release. Investigating their origin mechanisms not only advances our understanding of planetary stress accumulation and release, but also reveals deep dynamic processes, including tectonic activity and magmatism. Current research confirms ongoing seismic activity on Mars, providing a critical window into the planet's interior dynamics. The focal mechanism (strike, dip, and slip angles) directly reflects deep tectonic activity and serves as key evidence for understanding Marsquake triggering processes. While Earth focal mechanism inversion typically requires multi-station networks with good azimuthal coverage, Mars is currently limited to single-station data from InSight, posing significant technical challenges. The systematic evaluation of existing methods is crucial for developing novel inversion strategies for single-station observations. This study first reviews Earth-based focal mechanism methods, including those based on first-motion polarity, amplitude, and waveform fitting. Methods relying on first-motion polarity and amplitude require well-distributed station networks for complete focal mechanism sampling. For Mars' single-station inversion, P/S polarities and amplitude ratios alone cannot adequately constrain focal mechanisms. Waveform information must be fully utilized, with polarity/amplitude data typically incorporated into waveform-based inversions. The relative focal mechanism approach is suitable for analyzing clustered events-particularly relevant for Mars' regionally concentrated marsquakes. In waveform-based marsquake studies, velocity model uncertainties introduce challenges for full-waveform fitting. Seismic phase windowing with permitted time shifts during waveform modeling helps mitigate velocity model errors, making this approach (e.g. CAP) more viable for single-station inversions on Mars. Next, we summarize single-station inversion techniques (based on body waves, surface waves, full waveforms) developed for limited data on earth. Finally, we synthesize marsquake focal mechanism research, covering: 1) InSight mission background (instrumentation, data, Earth-Mars observational differences); 2) Tectonic setting (landing site, crust-mantle structure, stress field, thermal evolution); and 3) Research progress (methods, findings, unresolved challenges). In Mars focal mechanism studies, single-station waveform-fitting methods have been widely developed and applied, effectively addressing the insufficient sampling issue in single-station data. However, current results still exhibit significant uncertainties and inconsistencies across different studies, necessitating further optimization of inversion strategies. The clustered distribution of marsquakes enables the application of relative focal mechanism methods. Initial solutions obtained through waveform analysis can be further constrained using relative mechanism approaches. Earlier studies were limited by insufficient velocity structure and uncertain event locations, highlighting the need to update existing solutions using improved structural models and more accurate event locations. Through the comprehensive synthesis, we aim to provide methodological and theoretical support for single-station-based Marsquake focal mechanism research.