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The Mishnah in Masechet Shabbat (73a) lists memachaik as one of the 39 Avot Melachot.
- The melacha of memachek is defined as removing the roughness of a surface by smoothing or scraping after tanning. For example, scraping hairs off a piece of leather  or using sandpaper to smooth wood 
In the Mishkan
- In the mishkan, memachaik was performed to smooth the ram’s hides by removing the hairs as part of the processing of the leather 
- One of the toladot of this melacha is mimareach-smoothing not by eliminating surface, but by spreading something over the surface. 
- Mimareach doesn't apply in a case that the substance being spread is absorbed.  According to some poskim it doesn't apply if it will be washed away immediately
Cleaning Under One's Nails
- Some say that it is forbidden to scrap away the dirt under one's fingernails on Shabbat because of memachaik as it smoothes out the nail. Others are lenient as long as one doesn't scratch the actual nail.
- It is permitted to smear something over a piece of bread, such as butter onto bread. 
- One should not use a knife to scrape the mud off of leather shoes since you will inevitably smooth the leather. 
See Cosmetics page
- Rashi 73a, Rambam Hilchot Shabbat 11:5
- Gemara Shabbat 75b, Rambam Shabbat 11:6
- Yerushalmi Shabbat 7:3, 39 Melachot Rabbi Ribiat pg. 913.
- Rashi Shabbat 146a, Rambam Hilchot Shabbat 11:6
- Magen Avraham 316:24 writes that memareach only applies when you intend to spread one item on top of another. Accordingly, it doesn’t apply if the substance is absorbed. Mishna Brura 316:49 and Aruch Hashulchan 316:32 rule likewise.
- Chacham Ovadia Yosef (Sh”t Yabea Omer 4:30 about toothpaste and Yechave Daat 2:50 about soap) and Rav Soloveitchik (Nefesh Harav pg. 168) extend this to a case where the substance will be washed away immediately.
- Magen Avraham 161:5, Aruch Hashulchan 161:3, Ben Ish Chai (Shana Rishona, Kedoshim, no. 24)
- Eliya Rabba 161:5, Mishna Brurah (Biur Halacha 161 s.v. vehu), Kaf Hachaim 161:15, Halacha Brurah 161:4
- Kitzur Shulchan Aruch 80:58.
- Darchei Moshe 321:3 quotes the opinion of the Mordechai that just like the melacha of ibud, tanning, does not apply to food neither does Memachaik. Midirabanan there is ibud on foods, and this would be true for Memachaik as well. However, in the Shulchan Aruch 321:19, the Rama writes that if the food can be eaten without the smearing it is permissible. He adds that those who are stringent, are blessed. Mishna Brura 321:82 says that it is permissible to spread something over a piece of bread. In Biur Halacha “tavo alav bracha,” he adds another reason to be lenient based on the Smak that if you don’t intend to smooth but just want to cover the empty area, then it is permissible. The bracha to which the Rama refers is if you’re not smearing for eating but rather to make a nice design.
- Gemara Shabbat 141b, Shulchan Aruch 302:8, 39 Melachot pg. 914-915