Nuts can be stored in the freezer, which is a much better place for them than the pantry; because they are high in fat, their main enemy is rancidity, and cold significantly slows the process. Dried fruit can also be frozen, but because it contains more moisture, the pieces stick together; first freeze them in a single layer on a tray, then pack them in a bag.
Nuts do not spoil by molding or souring; they turn rancid. The oils in walnuts, hazelnuts, almonds, pistachios, and sunflower seed kernels deteriorate as they react with oxygen and heat. The resulting flavor is often described as paint-like or like old oil, and after it forms even one time, it cannot be reversed. Three factors speed up this reaction: heat, light, and air. A pantry cannot fully block all three, but a freezer almost completely removes the first and, when the nuts are packaged properly, blocks the other two as well.
That is why the freezer is the preferred place for nuts, not just an emergency option. Nuts that begin to taste stale after a few months in the pantry can comfortably last much longer in the freezer. Nuts in their shells last longer because the shells protect them, but the difference is much more noticeable with shelled or roasted nuts. Roasted nuts are especially delicate because roasting brings the oil to the surface and increases the area exposed to air.
Dried fruit is a little different. Although dried apricots, figs, raisins, dates, and plums look dry, they still contain some moisture; this moisture does not freeze but remains bound to the sugar, keeping the fruit soft. In the freezer, these fruits do not become rock hard, but they stick together in one mass. The solution is to freeze them on a tray: arrange the pieces in a single row on a tray without touching, freeze until firm, then transfer them to a bag. That way, you can take out as much as you want later.
Use the same packaging rule for both, and this is the most important part. Nuts and dried fruit absorb odors; they quickly pick up the smell of fish, onions, or a seasoned dish stored in the freezer. Use an airtight freezer bag with a zipper or a lidded glass jar, not a thin bag, and remove as much air as possible. Label the package with the date too, because you cannot tell by looking how long a frozen walnut has been stored.
Most of the time, there is no need to thaw them before use. Nuts can go straight from the freezer into a salad, cake batter, or breakfast plate; they warm up on their own within a few minutes. Watch out for condensation: when cold nuts are exposed to humid kitchen air, water droplets form on the surface, and the added moisture makes them lose their crunch. So take only the amount you will use from the bag, return the rest to the freezer right away, and do not leave the bag open in the kitchen. If you need to roast them, put frozen nuts straight into the pan or oven; they do not need to be thawed first.