Umm, from which angle would you be most interested in?
There are videos online showing how CRISPR/Cas9+sgRNA does its target recognition, and if you read the primary publications on the protein, they go into a lot more detail about its structure. I don't know if it's made its way into textbooks yet, but the canonical "CRISPR" isn't too hard to understand.
I'm not too sure about TALENs and ZFNs, the two older technologies for cutting DNA, but they've been around for a lot longer, and a few clinical trials are using them, so a quick google / pubmed search should find you a few reviews on them. The CRISPR field itself is only like 3 years old, too, so you can read through the most impactful publications in a relatively short amount of time.
Then there's homologous-directed repair (HDR) and non-homologous end-joining (NHEJ), which are the two primary mechanisms by which cells repair their genome after it has been cut. If you have a decent molecular biology textbook, it should have a section on DNA repair, which covers those two as well as a number of other pathways to repair damaged / mutated / mismatched / cut DNA. I've heard this topic is currently of interest within the CRISPR field, since people want more reliability / efficiency for the process and that involves better control over which repair pathways are used.
Beyond that, people are looking for better ways right now to engineer Cas9, including finding smaller versions of the protein from other species, generating Cas9s with alternate PAMs (The fixed start sequence that must be matched to the target DNA), making Cas9's that are photo-activatable / chemically inducible / "split" (Where the protein is cut into two sequences that bind each other to make a functional protein).
There's also research into the efficiency over different protocols, which I mentioned in the parent post, where the nuclease portion of Cas9 is mutated to a nickase / Link / Link / Link / Link, causing it to only cut one side of the DNA backbone. Thus you can have two sgRNAs that each target next to the site you wish to mutate, increasing the specificity of places in the genome that get cut on both sides of the DNA.
Another topic that's hot right now are Cas9-activators, where the protein itself is linked to transcriptional activators / epigenetic modifiers, allowing someone to up-regulate their gene of choice without having to modify the DNA. There's also Cas9-inhibitors, that down-regulate gene expression, but I don't think they work too well at the moment...
Lastly, there's the burgeoning field of synthetic biology, where people are exploring new ways to construct long sequences of DNA and create "gene circuits", where genes act together to sense, interpret, and respond to a cell's environment in predictable ways. Some of it is a little out there, but it can help to know about things like Gibson Assembly and Golden Gate, which are two useful techniques in assembling large portions of DNA.
Past that, knowing the basics of cloning / PCR / biochemistry / molecular biology will take you a long way. If you have a good foundation in molecular biology, you should be able to quickly learn any of the fancy biotechnology that's popular that year.
Hopefully that's not all too jargony, I kinda brain spewed there in an effort to get out the door in the morning faster.