There are many different kinds of yeast (one of the earliest organisms domesticated by humans) but there are some which are more prevalent than others.
For example, red yeast is not actually yeast at all but mold, so there is a lot of variety to take in to account. But for the most part you will likely just be dealing with bakers yeast and beer yeast also known as brewing yeast. Any by products of beer will ALWAYS contain gluten, so keep that in mind. However, most other types of yeast, such as baker’s yeast, active dry yeast, autolyzed yeast (but not it’s extract) and nutritional yeast, are ALL completely, 100% gluten free.
Nutritionally speaking, yeasts are very good at promoting antimicrobial and probiotic effects in people that consume product containing it on a regular basis. Those with gluten sensitivity or Celiac Disease should do their best to always read the labels and steer clear of brewing yeast and autolyzed yeast extract.
It is important to note that sometimes autolyzed yeast extract, and normal yeast extract, may be crafted from barley–which does NOT have to be labeled on the packaging, so keep a sharp eye.