There isn't really one authoritative "current definition" of a species the way we're taught in lower-level science courses, at least not one so clear-cut and universal. If you ask a molecular biologist, a botanist, a zoologist, an ecologist, a geneticist, and a paleontologist to define a species you'll get six different, and sometimes contradictory, answers. Hell, if you ask two biologists in the same field you'll occasionally get competing answers.

These different definitions are called species concepts, of which probably the most common is the biological species concept. This is the one that you're referring to, which defines species based upon reproductive isolation. But it's not a perfect nor universal definition; it's entirely useless for asexual organisms, isn't informative in cases of horizontal gene tranfer, can't be directly tested in certain circumstances like when dealing with fossil species, and even breaks down with extant sexual populations in situations like ring species or many cases of hybridization (which we're learning is a lot more common and complex than previously thought). Other species concepts work better when dealing with asexual populations, or extinct groups, or when working specifically at the genomic level.

Most biologists work within the framework of whatever species concept best fits their field day-to-day as a shorthand but recognize there's a lot of nuance to the biological reality. That is to say, it's not as simple as can interbreed or can't.