The dinosaurs first arose in the Late Triassic period about 225m years ago. No specific ancestral species is identified, but we recognise that there is a distinct lineage of animals that can be grouped together by shared features of their anatomy that we call dinosaurs. This group has three main lineages: the huge sauropodomorphs, the herbivorous and diverse ornithischians and the (mostly) carnivorous theropods.
Modern birds are the direct descendants of dinosaurs and so are part of the dinosaur group (or more technically, the dinosaur “clade”). Living birds are literally dinosaurs by definition.
This means several things, most obviously the fact that dinosaurs are not actually extinct. Most lineages of course have gone: every dinosaur lineage except the birds is extinct (and indeed various birds are no longer with us). Second, this means that when biologists and palaeontologists talk about dinosaurs, they actually generally mean all dinosaurs except the birds. This often goes unsaid in public communications (and occasionally the odd paper) but really when we say “dinosaurs” we should say “non-avian dinosaurs”. [more] image: Dave Hone
On a completely unrelated note, I challenge you to find me a bird more rockabilly than this.