In the middle ages in Europe, women would fight in time of emergency. Noblewomen were expected to organise and lead the defence of their own home and to lead their troops in the field if they had no male commander whom they could trust with the job (e.g. if they were a widow).
Crusades were pilgrimages as well as being holy wars, so women did 'take the cross' and join crusades, although those preaching the crusades preferred women to send money to finance troops instead of going in person. Their arguments were much the same as those now who argue that women should not fight in the armed forces: that women were not physically able to contribute to the military effort, they were a drain on resources, and their presence was a distraction to the men. As this was a pilgrimage they believed that it was particularly important that the men should not be distracted from their spiritual purpose; they ought to spend their time in prayer, but if women were with the army the men would be more inclined to spend their time in bed. Then God would be angry with them, and the crusade would fail.
Nevertheless, it is clear that many men took their wives and children - sons and daughters - with them on crusade. Some mothers took their sons. Women encouraged their husbands, boyfriends and sons to go on crusade and presumably some then accompanied them. The women acted as support forces, bringing water to the fighters and (presumably) applying first aid to the wounded. They assisted with basic labouring tasks within the camp, such as carrying earth to fill in the ditch around a besieged city. Women could operate stonethrowers, and use bows. Noblewomen could command the defence of a fortress, or finance and oversee the construction of a fortress.
It is not clear how far women fought in the field. Two Muslim sources tell us that women were found dead on the battlefield after a battle outside Acre on 25 July 1190. This account is so vivid that it appears to be true. The western sources say that only 'common people' fought that day, so these would have been ordinary women, fighting with the infantry. The western sources say that the common people had gone out deliberately without their noble commanders to attack the Muslims themselves because they had lost faith in the nobility to lead them effectively. In this case it is possible that some of the ordinary women (wives, sisters, daughters, mothers) went with the men as part of the common cause. The Muslims were profoundly shocked that the Christian women were fighting, as Muslim women did not fight except in very extreme circumstances, in defence of the home. Some Muslim chroniclers claimed that women were also fighting on horseback in the Christian ranks, as knights, and were identified as women when they were killed and their armour was removed. It seems very unlikely that Christian women would have fought as knights, mainly because the crusading commanders would not have allowed it - it would have been shame and dishonour for them to have allowed women to fight, as it was their duty to defend women, not for the women to defend them! What is more, it is very unlikely that such an event would not have been recorded by the western European chroniclers, partly because they would have enjoyed recording something so unusual. In addition, as the Third Crusade was ultimately a failure, the western European chroniclers were looking for persons or groups to blame for that failure. It would have been easy to have blamed the failure on the fighting women, but they did not. They never mentioned fighting women; therefore it is very unlikely that women fought on horseback during the Crusades.
We can imagine that the Muslims' story of women fighting on horseback, unrecognised beneath their armour, reflects Muslim amazement at the heavy western European chainmail armour which covered the whole body and the full-faced helmet which covered the face so that it was impossible to see what was inside it. The Muslims' armour was much lighter weight and did not cover the whole body, or the whole face. They must have wondered what nightmare creatures could be inside the European armour - fairies or demons? Or (horror) could they be fighting women? After the battle of 25 July 1190 it appeared that they might indeed be fighting women. In Muslim eyes, the fact that European women accompanied their menfolk on campaign and sometimes fought showed the utter depravity and barbarity of the Christians.
Further reading: see C. Maier, ‘The Roles of Women in the Crusade Movement: A Survey’, Journal of Medieval History, 30 (2004), pp. 61-82, for a survey of work to 2003.
For more detail on certain aspects of the subject, see for example my article on 'Women on the Third Crusade' in the Journal
of Medieval History, 23 part 4 (1997), pp. 335-49;
James Brundage has written on women on the first crusade: his paper 'Prostitution, miscegenation and sexual purity in the First Crusade' was published in Crusade and Settlement, ed. Peter Edbury (Cardiff, 1985) and reprinted in his collection of papers.
See also James Powell, 'The role of women in the Fifth Crusade',in The Horns of Hattin, ed. Benjamin Kedar (Jerusalem and London, 1992).
If you can read German, you should look at: Sabine Geldsetzer, Frauen auf Kreuzzuegen: 1096-1291 (Darmstadt: Wissenschaftliche Buchgesellschaft, 2003)
The best-known study of women on crusade is in R. C. Finucane, Soldiers of the Faith: Crusaders and Muslims at War (London, 1983), pp. 174- 84. This uses the sources uncritically and does not pause to analyse the Muslims' attitude to fighting women. See also Valerie Ead's 'Medieval Women and War' page.