The forward threshold voltage is where current conduction begins. Below this threshold current flow is negligible. For a silicon diode, voltage threshold for current conduction is about.5 volts. A commonly stated forward drop for the silicon diode is .7 volts. Forward voltage drop increases with a Log function, reaching about 1 volt at full rated current. In the reverse direction a diode doesn’t conduct much current. Minor leakage is present and varies as a function of temperature or light applied to the die.
Germanium diodes have substantial reverse leakage current. They offer very low forward drop. Front to back ratio was measured when technicians checked them using analog ohm meters (back when germanium was more popular, ten to one front-to-back ratio was a passing value). Shotkey diodes are similar to germanium diodes. Both offer fast recovery time. Low voltage ratings limit the use of both.
Reverse breakdown voltage is where avalanche breakdown causes a reverse biased diode to become conductive. Reverse voltage breakdown testing can be destructive. Avalanche rated diodes can be placed in series without adding an external compensated resistor divider. Fast and ultra fast diodes are usually avalanche rated.