Unfortunately vintage knitwear is generally hard to find, and expensive when you do, so we often have to rely on the high street for a reasonable imitation of vintage styles. This is just the briefest of overviews of the three 'main' decades (the ones that most vintage-wearers favour), intended primarily as a guide to help define some of the key features to look out for when shopping the high street for vintage-looking sweaters. Indeed, you might be surprised at how modern some of these look.
There are also some repro knitwear companies - Rocket Originals are my absolute favourite, though they're made in acrylic and acrylic blends.
Mid-1930s sweaters - like the dresses of the era - often featured extravagant collars and jabots. Sleeves were either long (note the long cuffs) or short and puffed. Dressier styles were blousy over a fitted waistline, while casual knitwear was unfitted and boxy, and cut long.
Throughout the 1940s knitwear necklines were high and rounded (bad news for the large of bosom looking for a flattering-yet-authentically-vintage style, I'm afraid). Short sleeves are puffed in the early 40s, but lose their puff in the postwar styles. The silhouette is semi-fitted, finishing a little below the waistline.
knitting pattern, c early 40s
In the 1950s there's a lot more neckline variation coming in - from Peter Pan collars to V-necks (with jaunty neck scarf), square necks, turtlenecks and roll collars. The dolman and Raglan sleeve styles are fashionable around the middle of the decade. Sweater wasitlines sit on the waist or just below; cardigans finish a little lower. Bolero cardigans are popular for dressy wear.
While I'd always recommend wool and cashmere for warmth, from the 1950s onwards acrylic is not only washable and easy to find in modern knits, but also perfectly authentic, having been commercially available since the early 50s.
Knitting pattern, c early-mid 50s