Did the Church Fathers advocate celibacy? What is an overview of the Church Fathers' views on celibacy? Did they see celibacy as a higher or more spiritual calling than marriage? Did they see marriage as incompatible with a spiritual life? Was there general consensus or was opinion split?
The general consensus, following Paul's teaching, seems to be that marriage is good but celibacy is better.

Tertullian may have been the first to write about it:


  In short, there is no place at all where we read that nuptials are prohibited; of course on the ground that they are “a good thing.”  What, however, is better than this “good,” we learn from the apostle, who permits marrying indeed, but prefers abstinence; the former on account of the insidiousnesses of temptations, the latter on account of the straits of the times.


Chrysostom, in his homily on 1 Timothy 3, explains the biblical rules for bishops:


  “A Bishop then,” he says, “must be blameless, the husband of one wife.” This he does not lay down as a rule, as if he must not be without one, but as prohibiting his having more than one. 


He later elaborates:


  If then “he who is married cares for the things of the world”, and a Bishop ought not to care for the things of the world, why does he say the husband of one wife? Some indeed think that he says this with reference to one who remains free from a wife. But if otherwise, he that hath a wife may be as though he had none. For that liberty was then properly granted, as suited to the nature of the circumstances then existing. And it is very possible, if a man will, so to regulate his conduct. For as riches make it difficult to enter into the kingdom of Heaven, yet rich men have often entered in, so it is with marriage.


He adds:


  “They that are Christ’s have crucified the flesh”; and Christ again says, “Whosoever forsaketh not all that he hath, he is not worthy of Me.” Why are not these things required by Paul? Plainly because few could be found of such a character, and there was need of many Bishops, that one might preside in every city.


So Chrysostom agrees that celibacy is better, but regards monogamous marriage as a practical alternative.

Evidently in Augustine's time, a monk named Jovinian wrote that celibacy was no better than marriage. Augustine responded with a treatise, On Holy Virginity, then, fearing he might be misunderstood, wrote another, On the Good of Marriage. [secondary source, can't find link to originals.]