Horseshoe Crabs represent a long and proud lineage of chelicerate arthropods. Famed for their role as survivors, the order Xiphosura (fancy word for horseshoe crabs) can trace their fossil record back to the Ordovician Period some 445 million years ago. A once diverse lineage of animals, today xiphosura is represented solely by the Atlantic Horseshoe Crab Limulus polyphemus. Traditionally it has been hard to place the Horseshoe Crab into the evolutionary tree of life. Many studies have concluded that the Horseshoe Crab is a distant relative of arachnids. However many of these studies were going in with a biased assumption, arachnids are a monophyletic group of organisms.
In evolutionary biology, phylogenies are created using various datasets to reconstruct the evolutionary relationships between different organisms. When a selected group of organisms can trace their heritage back to a common ancestor, we call this group monophyletic. A good example of a monophyletic group is the Primate Order. All living primates share a common ancestor as consistently indicated by both fossil/morphological datasets as well as genetic datasets and are therefore a monophyletic group of organisms. Things can get messy with recovering the phylogenies of organisms with broad and unclear relationships that originated deep in time. Such is the case with chelicerates.
You and I are both fish, in a taxonomic sense, as are all terrestrial vertebrates. We can trace our ancestry back to boney fishes in the Devonian and many features we take for granted, such as our ears and Adams-apple are highly derived gill ridges. Obviously though, when I tell you that I'm going to spend a weekend fishing, you the reader aren't confused by evolutionary semantics and envision a set group of animals. Perhaps if I say I'm fishing at a lake, you the reader would envision me reeling in a trout or pike. If I say I'm going to fish at sea perhaps you the reader envision me reeling in a tuna or a shark. You don't however, envision me catching an elephant nor a kangaroo when I say "I'm going fishing" despite both organisms being *fish* in the evolutionary sense as their ancestry is ultimately bound to the water. The same applies for reptiles, most people generally view reptiles and birds as separate categories of organisms. This division between birds and reptiles falls apart when one considers that birds are dinosaurs and dinosaurs are clearly reptiles. Paraphyly refers to when a large group of animals are given a name/rank but selected subgroups are omitted due to differences in bodyplan or ecological habit. So whenever you call something a "fish" but are failing to include every other terrestrial vertebrate in your referral, you are being what taxonomists call "paraphyletic".
Chelicerates should be defined before we go any further as things could get confusing quickly. Today the chelicerates include the following; mites, spiders, sea spiders, harvestmen, scorpions, pseudoscorpions, camel spiders, whip scorpions.... You get the point. The exact relationships between the sub-categories of the chelicerates is a bit messy, it was long assumed that chelicerates include a monophyletic "arachnid" sub-group with xiphosura being its sister out-group clade. Genetics has brought into question that assumption. Most morphological studies recovered a monophyletic arachnid group with a sister monophyletic Xiphosura clade.
Genetic analytical work by Ballesteros et al. has shown however that many of the "arachnid" groups are are not related closely to one another and are instead convergent. More interestingly the study found Xiphosura to be nested smack-dab between Opiliones (harvestmen/daddy longlegs) and Pseudoscorpions both of which are traditionally considered arachnids. This result is interesting as it implies that the traditional definition of "arachnids" is a paraphyly. To recover arachnids as a true monophyly, the definition would need to be expanded to include Xiphosura, meaning that Horseshoe Crabs are arachnids.