Israel has, over the last few decades, expanded the number of combat jobs women can volunteer for. Israel conscripts men (for three years) and women (for two years). But women have more exemptions (especially marriage). Women who volunteer for combat duty are hard core, because not only will they have to undergo some hard training, but will have to serve three years on active duty, plus several years as reservists. This is necessary to justify the longer training required.
Like many other countries, Israeli military police units contain men and women. Same with dog handlers, border guards, artillery units and some search and rescue units. Women have long served as flight instructors, as well as trainers for tank crews.
There is also a largely female infantry unit, the Caracal Battalion. Part of the 512th Brigade in Southern Command, the battalion was formed in 2000 to provide a place for women who wanted to be in the infantry. It's a light infantry units that mainly serves along the Jordanian or Egyptian borders. The battalion took part in safeguarding Israeli civilians and troops during the 2005 evacuation of Gaza. Initially, about half the troops in Caracal were female, as are most of the officers and NCOs, and, usually, the commander. Now about 90 percent of the Caracal members are women. While many troops see Caracal as a publicity stunt and a sop to the feminists, the unit has performed well, and has a reputation as a non-nonsense and reliable outfit.
During their independence war in 1948, Israel had female infantry units, but these were withdrawn. Not because the women couldn't fight, but because Arab units facing them became more fanatical, and less likely to surrender, when they realized they were fighting women. Conservative Jewish clergy in Israel want women to be barred from combat jobs, while Arab radicals are urging more women to get involved in terrorism operations, including suicide bombings.