We recently posted on reports of the re-evolution of traits that had long been lost in evolutionary time. This seemed to violate Dollo's "law" that evolution was a one-way train that couldn't back up.
But there are reasons to think that true reversibility of complex traits can't often happen over evolutionary time. The basis of the argument is that too many genetic changes are required for a complex trait to be constructed and if the trait is 'erased' by mutation (and that is supported in the face of selection), then over time too many other genetic changes (mutations, gene duplications, other uses of genes, etc.) will make it impossible to back-track.
From this point of view, the 'new' version of the trait is physically similar to the old, or to that in a widely distant species, but is due to selection for the same trait that happens to pick up different genes and alleles to get the job done. But if a pathway has been conserved because it's used for other things in the organism, it may be that simple genetic changes can reactivate that pathway in a context in which it was active long ago.
There has been a similar kind of no-going-back dogma, a kind of Dollo's "law" in developmental genetics. Stem cells can differentiate into anything, but once that happens, the differentiated cells simply cannot go back to being stem cells. We now know that this is not accurate. Even a small number of genetic changes in experimental systems can restore various stem-cell states. This can happen even if the cell being manipulated is highly differentiated. Is this as surprising or inexplicable as reversals in evolution?
The answer is that it is far less surprising, as a generality. With some few notable exceptions, all the cells in your body have the same genome. This means that while each cell is of a particular type largely because it uses a specific set, but not all, of the genes in the genome. There are, so to speak, 'blood' genes, 'stomach' genes, and so on. Gene expression is based on the physical packaging of chromosome regions and the presence of proteins specific to the cell type, that bind to DNA in regions near to, and that cause the expression of the specifically used genes. But since with few exceptions all the genes still exist in all cells, if one changed these regulatory traits (packaging and so on of DNA, presence of regulatory proteins), one could make the cell do something else. There may be too many changes in expression needed to make a stomach cell into a lung or muscle cell on its own, but we're looking at cells from the outside, and cells can be engineered to redifferentiate or dedifferentiate by experimentally imposing required sets of change. And in a sense it's why in some instances it only takes about 4 genes being manipulated to bring cells back to a very primitive stem cell type of state.
Evolution is different, because once a species is committed to a particular direction, its genes themselves as well as their usage have changed, by virtue of mutation and frequency change induced by chance or natural selection. Thus, spiders and grasshoppers no longer have the same genes so that only the expression pattern would need to be changed to let spiders hop or grasshoppers spin webs. That is why evolution rarely truly reverses. Sometimes only a few changes would be needed, if basic pathways still exist but have been mutationally inactivated.
On the other hand, most traits have many paths and most genes have many uses, so that there can be many different paths by which some absent trait--or its likeness!--can reappear. Natural selection and chance could activate some suitable set of genes to make this happen, and how likely it is depends on what environmental constraints are. And since many developmental genes are highly conserved over long time periods, there can easily be similarities in the genetic basis of reappearance.
We know that some traits, such as complete vs incomplete metamorphosis in some species of amphibians (i.e., whether or not they go through a larval stage), or the pattern of ocelli (middle eyes) in insects, have re-evolved. And we know that some genes from mammals can induce similar effects even in insects, by replacing or over activating their corresponding insect gene.
So, reversals are of many types due to many causes. How likely they are, and how genetically they are brought about, are statistical and context-specific questions. But there are no real mysteries about whether or not they are possible.