How did multicellularity evolved?
It is an ongoing field of research - Some insights about the origin of multicellularity
This is a big ongoing field of research. To start with an example, there was relatively recently (2012) an important article by Ratcliff et al. that shows that yeast can quickly evolve multicellularity under selection on the speed they sink to lower water layers. This article is one among many others and is far from being able to explain everything we would like to understand about the evolution of multicellularity. Typically, I think that this yeast species had a multicellular ancestor and we might think that this species would already have fixed alleles (=variants of genes that is fixed meaning that the whole population is carrying this variant today) in the population predisposing this species to easily (re-)evolve multicellularity. Also they may have kept some standing additive genetic variance in their genome from their past and they would therefore very quickly respond to selection as they don't need de novo mutations. (Sorry if this last sentence was slightly technical).
One of the first trait that we usually refer to when talking about the evolution of multicellularity is the presence of sticky proteins allowing individual cells to paste to each others.
Some insights about the evolution from simple multicellular to more complex multicellular
Then, we could talk about more complex multicellular and argue how do these simple multicellular evolve into some more complex organisms. A common argument is that multicellular can have specialized cells are are very could at doing what their doing as they are specialized. Also, some level of complexity is thought to have raised due to the fact that multicellular organisms tend to have smaller population size than unicellular (see Lynch and Conery, 2003). It is important not to confuse evolution of complexity with evolution of multicellularity although these two notions are somehow related.
What do you mean by multicellularity?
The evolution of multicellularity can be discussed in the context where sister cells form an organism together or when unrelated cells (among the same species or even cells from different species) come together to form an organism. Also, the multicellularity can be discussed at different level depending on how we want to define multicellularity. Is a stack of cells reproducing individually, working for their own benefit a multicellular? Do we need division of labor? Do we need division between germline (reproductive caste) and soma line (non-reproductive case)?
How many times did multicellularity evolve independently?
Some people consider that there are multicellular bacteria (biofilms) but we will avoid discussions that are based on limit-case definitions. Let's talk about eukaryotes. Most Eukaryotes are unicellular and multicellularity evolved many times independently in eukaryotes. To my knowledge, complex multicellularity however evolved only (only?) 6 times independently in eukaryotes.
- Metazoa (animals)
- Ascomyceta (fungi)
- Basidiomyceta (fungi)
- Viridiplantae (green plants)
- Florideophyceae (red algae)
- Laminariales (brown algae)
Model organisms and interesting cases to study multicellularity
There are a bunch of specific clades that are particularly interested in studying multicellularity because they present transition states. For example Volvox is a chlorophyte genus and the species in this clade present different stages of multicellularity; Some species are exclusively multicellular, some form small groups, some create big colonies, some have some division of labor and some even have separation between the germline and the soma (Some castes don't reproduce). (ref1, ref2, ref3, ref4, ref5, ref6). Yeasts are also good model organism for studying the evolution of multicellularity.