Semiconductor　germanium　(Ge)　in　contact　with　some　metals,　such　as　Al,　Pd,　and　Au,　etc.,　is　a　class　of　distinctive　materials　with　non-integer　dimensions　(D)　that　differ　from　integer　dimensional　materials,　such　as　nanoparticles　(0D),　nanowires/nanorods//nanotubes/nanoribbons　(1D),　and　thin　films　(2D).　In　this　article,　we　describe　our　efforts　toward　understanding　the　annealing　strategies　and　perspectives　of　metal-induced　crystallization　for　the　amorphous　Ge　embedded　in　Al,　Pd,　and　Au　matrices　prepared　by　high　vacuum　thermal　evaporation　techniques,　highlighting　contributions　from　our　laboratory.　First,　we　present　the　Al-induced　crystallization　of　amorphous　Ge　and　formation　processes　of　fractal　Ge　patterns.　In　addition,　the　fractal　Ge　patterns　induced　by　Pd　nanoparticles　with　solid-state　reactions　will　be　summarized　in　detail.　Temperature-dependent　properties　of　resistance　and　fractal　dimension　in　Pd/Ge　bilayer　films　will　be　expounded.　In　particular,　the　nonlinear　optical　properties　are　discussed　in　detail.　Finally,　we　will　emphasize　the　in　situ　observations　by　transmission　electron　microscopy　and　multi-fractal　analysis　for　the　fractal　Ge　patterns　induced　by　Au　nanoparticles.　Moreover,　the　polycondensation-type　fractal　Ge　patterns　with　non-integer　dimensions,　thick　branches　and　smooth　edges,　and　metastable　gamma-Au0.6Ge0.4　are　further　investigated.　The　computer　simulation　indicated　that　the　experimental　results　are　good　agreement　with　the　simulation　patterns,　which　were　carried　out　by　a　ripening　mechanism　of　non　uniform　grains.　This　review　may　provide　a　novel　insight　to　modulate　their　competent　performance　and　promote　rational　design　of　micro/nanodevices.