It's not just semiconductors, or even electronics in general. It's everywhere in the supply chain.
For example, we're having trouble sourcing certain kinds of connectors. We finally found some pockets of stock as far away as the Netherlands and brought those in. (Related warning: Arrow is inconsistent about informing you of tariffs! When you order via their website they don't always tell you where in the world the parts they're offering are stocked, and if they happen to fulfill from overseas you can get hit with a substantial tariff by the shipping company which Arrow will deflect, deny, and ignore. In this order I'm talking about FedEx hit us with an unexpected 25% tariff and Arrow would do nothing about it. Other vendors have this figured out, and in talks with other Arrow customers we are not the only ones to be surprised this way.)
Our experiences with chips is similar to what others have reported here. We have purchased from the grey market in the past and a couple of those vendors have been able to help us, though at a 3-4X markup.
But by far the worst one for us is the hydraulics industry. We have a new product line, five years in development, which includes some hydraulics and was due to enter production this June. Back in 1Q2021 we started working with the hydraulics supply chain to prepare for production to start in June and were informed that components which generally have ~4 week lead times were (direct quote) "26 weeks and no promises". Translation: They might be able to get you some of your order in six months but don't count on anything. Since then we can't even get prototypes nor Engineering samples of otherwise off-the-shelf parts like pumps and motors. That's no way to introduce a new product line, so we have lost an entire year's production thanks to these supply chain effects. It's maddening.
I personally dug into the hydraulics problem and learned that it's all ripple effect. Back at the start of COVID-19, the hydraulics industry - just like the automotive industry - tapered their forecasts and cancelled orders because they expected demand to fall. What are their vendors going to do, let their factories and foundries sit idle? Nope, they sold that capacity to other industries who were more than delighted to absorb it. Fast forward a few months and demand never fell off, but when the manufacturers went back to their vendors the ripple effect had done its damage. In the case of hydraulics, pumps and motors have casings which are made from cast metals. The hydraulics companies had cancelled orders with the casting houses, so the casting houses had cancelled raw metal orders with their foundries, so the foundries contracted that capacity to other industries. Now the casting houses can't get metal, so the casting houses can't provide castings to the hydraulics manufacturers, so the hydraulics manufacturers can't get castings to make into pumps and motors.
Here's another example. Some of our customers manufacture boats. They're production lines are stalling and can't ship product because of random shortages. One day it's windshields. Another day it's billet aluminum parts. One casually mentioned a while back that they had otherwise completely finished boats filling the parking lot because they were missing a single component: A $6 horn that comes from China. These are ~$100K+ products being held up by a six dollar part. That industry is also having trouble finding gelcoat, resin, and other things related to fiberglass partly due to the Texas power outage which shut down refineries that produce such things.
Just In Time manufacturing sounds great, until a single link in the chain hiccups. Then the entire house of cards falls and the ripple effects can take weeks or months to sort out. What's sadly funny about this is that I've had discussions about JIT with our customers many times when things were "normal" and their comments inevitable get to "We spend more than JIT saves us on expedite fees and overnight shipping". JIT makes the MBA's and beancounters happy but it's a nightmare for Purchasing, Production, Sales, Customers, and Engineering (the latter when we get sucked in to "find an alternative NOW!").
We've always been a little obsessive about planning for shortages so we've been a bit better protected than others, but we're struggling too with several parts. In one case where a PCB revision was scheduled anyway, we are going even farther than normal and putting in 0R "jumper" resistors which we can selectively stuff to accommodate footprint-compatible, "almost" pin compatible alternatives for certain IC's. It's a kludgy way to design things but if we can't ship product we won't have a company. The one thing to avoid is overreaction - like others here have said, this has happened before and you can get whip-sawed redesigning for what's available today only to find that the shortages have moved tomorrow.
The takeaway message here is that we are in a technically advanced industry that has many, extremely interdependent tendrils. Disruption in any one of them can cause ripple effects to your whole company. Wise Engineers will design products to accommodate multiple sources, which isn't a guarantee but can soften the effects. For example, we've been known to have multiple footprints on a board for the same basic part from different vendors... we buy what's available for each production run and revisit that decision with each run, and the firmware either determines today's configuration or the boards are selectively flashed based on the parts installed. This isn't the first, nor the last, time this has happened so when possible, design accordingly.