Quasi-Z-source　inverter　(qZSI)　with　wide　range　voltage　boost　capability　is　suited　to　the　application　in　the　renewable　energy　power　generations.　This　review　introduces　the　development　and　the　present　of　three-phase　voltage-fed　qZSI,　covering　circuit　topologies　and　modulation　techniques.　The　three-phase　voltage-fed　qZSI　topologies　are　categorized　into　two　classifications:　1)　single　impedance-source　qZSI　topology;　and　2)　the　extended-boost　quasi-Z-source　network.　The　modulation　techniques　including　SPWM,　SVPWM　and　modified　SVPWM　for　decreasing　leakage　current,　are　advanced　to　the　three-phase　voltage-fed　qZSI.　It　also　gives　the　performances　of　output　waveform　quality　and　DC　input　voltage　utilization　for　the　different　modulation　techniques.