Inverse　modeling　of　microwave　components　plays　an　important　role　in　microwave　design　and　diagnosis　or　tuning.　Since　the　analytical　function　or　formula　of　the　inverse　input-output　relationship　does　not　exist　and　is　difficult　to　obtain,　artificial　neural　network　(ANN)　becomes　an　efficient　tool　to　develop　inverse　models　for　microwave　components.　This　paper　provides　an　overview　of　recent　advances　in　neural　network-based　inverse　modeling　techniques　for　microwave　applications.　We　review　two　different　shallow　neural　network-based　inverse　modeling　techniques,　including　the　comprehensive　neural　network　inverse　modeling　methodology　and　the　multivalued　neural　network　inverse　modeling　technique.　Both　techniques　address　the　problem　of　nonuniqueness　in　inverse　modeling.　We　also　provide　an　overview　of　recently　developed　hybrid　deep　neural　network　modeling　technique　and　the　application　to　inverse　modeling.　For　the　inverse　modeling　problem　with　high-dimensional　inputs,　the　relationship　between　the　inputs　and　the　outputs　of　the　inverse　model　will　become　more　complicated　and　the　inverse　modeling　problem　will　become　harder.　The　deep　neural　network　becomes　a　practical　choice.　The　hybrid　deep　neural　network　structure　is　presented.　The　recently　proposed　activation　function,　specifically　for　microwave　application,　and　a　three-stage　deep　learning　algorithm　for　training　the　hybrid　deep　neural　network　are　reviewed.