Leon-E. Halkin's Erasmus parmi nous, translated by John Tonkin as Erasmus: A Critical Biography, gives a full account of Erasmus's life and works. I am glad to have read it. The author seems a little anxious to emphasize the orthodox side of Erasmus and play down any skepticism one might suspect. The book as I read it seems to me to suffer from a number of drawbacks.
First, that the work is a translation. Mr. Tonkin's French must be vastly better than mine. Yet here and there I find sentences that make me suspect that something is missing. Then I wish for a sight of the original. Still I know that reading the original would take longer and that in reading it I would make far more mistakes.
Second, that in his advocacy for Erasmus, the author ignores the claims of some of what Erasmus opposed. It is well to mock the ossified end of scholasticism; but Halkin mentions Scotism in passing, dismissively. The nineteenth-century American philosopher C.S. Peirce thought highly of Duns Scotus. On some matters of faith, Erasmus, or maybe just Halkin, seems reluctant to consider what Jaroslav Pelikan refers to as the lex orandi, theology as informed by the prayers of the faithful.
Third, that a biography of a writer ought to live through the writer's words, and this is not practical for a life of Erasmus. His writing was all in Latin, and I don't suppose that the flavor can be wholly brought over into English. Some writers have an adventurous enough life to sustain interest without regard to their writing: Stendhal, Tolstoy, and Hemingway come to mind. But Erasmus mostly wrote and worried about getting together enough money to let him continue to write and publish.
John Huizinga wrote a somewhat shorter book on Erasmus, available in English as Erasmus and the Age of the Reformation. My copy is gone, for it was falling apart when I bought it. Huizinga has a lighter touch, is unburdened--in my recollection--by any commitment to Erasmus's commitment to orthodoxy, and perhaps had a better translator--or perhaps Dutch comes more naturally over to English than French does.
Pelikan gives a brief notice to Erasmus in his The Melody of Theology. His judgments on Erasmus are in the end not that much different from Halkin's. Of course his judgment on the scholastics--represented in this book by Aquinas, not Scotus--takes their strengths into account as well as their weaknesses.