When the Talmud discusses how a bris milah is performed, it mentions three stages - milah (excision of foreskin), priah (removal of mucosal membrane from the glans), and metzitzah (drawing of blood from circumcision spot, following the acts of milah and priah).
In order to do each of these properly, different surgical instruments and methods have been created or introduced over time to make the experience easier for the mohel, and, in consequence, for the baby.
All of these have been addressed before, but here are the links for the items utilized, presented in their order of use - each has its own "debate" attached to it, summarized as briefly as I can
NUMBING - to numb or not to numb, that is the question. There are those who argue it is forbidden. Those who argue it is obligatory. And those who say it is optional. (And those who argue that injections cause more pain to the baby than the circumcision, and that a topical cream does more for the parents than for the baby (who will cry anyway), as cream makes things more slippery (not a good ingredient for something precise as circumcision)
GLOVES - to wear or not to wear, that is the question. There are those who argue it is forbidden (never done before, chatzitzah). There are those who argue it is obligatory (sterility). And there are those who argue it is inconvenient (slippery, or can't do priah properly). See this article by Rabbi Aryeh Leibowitz, in which he weighs all the pros and cons.
MARKER - to mark or not to... (OK. I won't use the joke anymore). I can't even present the side against this, because it is beyond stupid. Anyone who argues that marking the edge of the foreskin with a surgical pen is anti-tradition is a full-scale idiot. I've seen too many babies have either not enough, too much, or an uneven (right v left sides) amount of skin removed, a problem alleviated by just using a little common sense plus a marker.
PROBE - The probe is used to separate the membrane from the glans so the circumcision can more likely remove the membrane at the same time as the foreskin. Those who don't use a probe argue that it is painful. And then they stick their fingernails underneath the foreskin to accomplish the same job. 😑.
HEMOSTAT - The hemostat allows for two of the stages of Bris Milah to be accomplished in one action - what is known in Hebrew as מילה ופריעה בבת אחת. Very skilled mohels often do this when they grab the foreskin with their fingers. Otherwise the hemostat grabs them together. Those who are against it are adamant that the two stages be done separately, AND that priah be done using fingernails - tearing the membrane and folding it beyond the corona, AND they argue that the hemostat is painful to the baby. Those who use it argue that there is an ancient tradition of doing Milah and Priah at the same time, AND that tearing the foreskin with fingernails (method of those who don't use a hemostat) is also quite painful, AND that NOT removing all of the priah membrane could cause problems for the child down the line, either as a child or an adult requiring corrective skin removal surgery. In other words, the pain argument is a question of quantity and degree against both sides (short term v long term e.g. corrections)
SHIELD - The use of the traditional Shield is a hallmark of most Orthodox mohels. Its purpose is to isolate the foreskin (what we are removing) from everything else that we don't want to touch (shaft, glans, scrotum, etc) Some who do not use it opt for a clamp, which accomplishes the same thing in terms of protection (when used properly) but it has its own halakhic, hashkafic and safety issues. Others who do not use the shield do the entire procedure freehand, putting everything near and dear to the baby's safety at risk. As to the clamp - I don't use it nor do I recommend it. I've written plenty of things against clamps in this website. As to the shield, those who argue to use it are concerned for the baby's safety and are doing their due diligence to protect the baby from an unfortunate mishap. Those who argue against it claim that it hurts the baby (see previous paragraph for cost/benefit ratio question), and that it's an innovation from 400 years ago (or so) that has no place in this ancient tradition.
KNIFE - The idea behind using a double edged knife is based on a "drasha" from the verse וחרב פיפיות בידם. In general, the sharpest knife should be used, so the incision is as quick as possible. Using a double-edged knife is entirely a hashkafic issue, as the rules of bris say anything can be used to excise the foreskin (except a reed which could give the baby a splinter), "but the custom is to use a knife."
TUBE - Metzitzah, the third Talmudic stage of the bris, can be accomplished in a number of ways. The most common methods utilize the power of the mouth, while the less common method uses a sponge or gauze. The most common methods either have the operator putting his mouth directly on the open wound, or have a sterile tube serving as a barrier between baby and mohel. Both of these methods are halakhically "metzitzah b'peh (or b'feh)," while hashkafically, the tubeless method is deemed by purists to be the "only acceptable method." To those who are sterility conscious, the tubeless method is wholly unacceptable - potentially putting baby, and sometimes mohel, at risk of spreading an infectious disease. In this view, metzitzah should be done with a sterile tube.
This post is in response to a recent phone conversation I had with a new father in Florida who personally was interested in the circumcision taking place, but did not particularly care about methods - only results. His parents, however, who hail from a very right-wing Orthodox community in the Northeast, carry every hashkafic notion of bris in a manner that clearly views other methods as unacceptable. As a colleague of mine told me, "If people ask, you let them know that 'hiring me means you get this kind of service, and if you don't want that, hire someone else.'"
Not that I believe for one second that anyone wants any harm to come to a baby. However, a hashkafa that proclaims that achieving circumcision results using methods that don't conform to safety and sterility are IDEAL - when I have heard plenty of stories from people who had very negative consequences (hospital visits, infection, baby on antibiotics post bris) - troubles me personally and deeply.
My method, thank GOD, has a perfect track record in terms of no-infection post-bris. Because everything that needs to be protected is protected, and nothing is exposed to bacteria that could have negative consequences.
I certainly wish everyone well, and hope that everyone hires the right mohel for their purposes, with the best interests of their baby in mind.