@Ernest BywaterHistorically, the ban on priests being married has waxed and waned. The first ban on it began in the fourth century. At the same conclave women were first banned from the priesthood. That was more strictly enforced but, again, was never totally enforced for extended periods. The most consistent ban on married priests has been among the Jesuits. In the 17th and 18th centuries married priest in other orders were nominally banned but if they married they were expected to be faithful husbands and support their wives and families. They couldn't rise in the priesthood and were often relegated to the role of curate in a smaller parish or, rarely, priest of a small, usually rural, parish. Even now, if a Lutheran, Anglican, or other "mainstream" Protestant married minister converts to being a Catholic priest he can remain married. Occasional other exceptions are granted but not commonly acknowledged. I have found some claims that not marrying is not a part of their vows per se, but, rather, a promise to the Bishop officiating their ordination. Likewise, I can't find confirmation to the claim that priests in Africa are given a blanket permission to marry or if it's just individuals to whose marriage a blind eye is turned.
Also, there has almost always been a very small but fluctuating number of ordained women priests. In the last century it has usually been to cope with special circumstances such as supplying priests in Soviet Women's prisons.