Regrettably, most of the wood edge, understory and blocking roadside shrubbery you see in the Midwest is Asian Bush Honeysuckle (ABH). ABH consists of a couple of species, with non-fragrant flowers ranging from white to red-pink, with hints of yellow, and they hybridize. All are horrible invasive nonnative woody species. Every landowner should do what they can to rid or reduce this scourge on their property. If not, it/they WILL take over. There are literally billions of ABH plants in central Indiana. The species have been in the US for almost 300 years but has only recently (last few decades) have become a naturalized nightmare. It is now ubiquitous.
ABH is one of the first woody species to leaf out in spring with opposite, tapered leaves and the new flush at the stem tip will have a coppery blush. ABH is one of the last species lose its leaves in the fall and is a prolific fruit producer. Birds help spread the seeds in the multitudinous pretty red (sometimes orange) berries but derive little nutritional benefit--more like candy (high in carbs, low in proteins and fats). Moreover, like many members of the honeysuckle family (Caprifoliaceae) ABH can and does spread asexually. When the branches come in contact with soil, they layer root permitting the plant to slowly walk across the landscape, like its close relative Forsythia. And ABH can get big. The main trunk of some specimens I removed from my property in Indy during the last decade were over 20 inches in diameter and well over 15 feet tall. Moreover, the heavily shaded ground beneath the overarching canopy of larger specimens is largely devoid of other vegetation because ABH is also allelopathic (i.e., it produces compounds that inhibit the growth of other plants). Allelopathy is a phytochemical defense strategy. Many species do this, with black walnut being the most well-known example.
So, how do I get rid of this invader? Many people try to do so by spraying herbicide. While this may occasionally be part of the solution, I DO NOT recommend it for the average homeowner. WHY? Several reasons: the herbicides are expensive and nonselective, they can pose a health hazard to animals, and you will still be left with a woody skeleton.
Another ill-advised method is to simply lop the stems at or near ground level. Unfortunately, this seldom kills the plant. This is a cultivation (pruning) action--not an eradication action. The specimen will resprout and you are left with a stump to stub your toe or to trip on. Moreover, if you do try this method, be certain to prevent the specimen from reestablishing by breaking off or cutting the new sucker sprouts as they develop. This will eventually starve the plant.
The method I use and promote is manual removal of the whole plant, including the main portion of the root. There are devices to assist in the removal, but I find them awkward to use and store and they are somewhat expensive. Instead I use a cutting mattock and elbow grease. There is a pick version of the mattock, but the ax form is what you want. And, since ABH produces lateral roots rather than a taproot, the grubbing is relatively simple for smaller specimens (i.e., <4" diameter). It simply requires effort. Cutting mattocks are available for about $20 at most hardware stores. It is a must have gardening tool. FYI: You will eventually discover that the main body of the ABH root will extend in one direction, and that if you pull or bend the stem in that direction relatively large specimens often can be extracted without grubbing. I also use a pruning saw and chainsaw to gradually dismember larger specimens. And, when trying to remove the root portion of a woody specimen (any species), it is a good idea to leave 2-3 feet of stump for leverage.
So, what to do with the woody skeleton including the excavated root? I have discovered that ABH burns green. I have incinerated lots of it. However, do not put the ash on your vegetable garden or flower beds, and be ever vigilant to remove any seedlings which appear. Unfortunately, ABH is here to stay. But we do not have to like or tolerate it on the property we maintain. Be a good land steward. Get rid of this awful invader and promote native alternatives like the formerly more common, shade tolerant and closely related native coralberry (Symphoricarpos).