Cut-and-thrust fencing is a style of swordplay intermediate between the cutting-centered days of the longsword and arming sword and the tight thrust-oriented play of the rapier. The sword used was straight, was shorter than the longsword but with a similar aspect ratio/rate of taper, and usually featured a few simple rings protecting the fingers and hand that gripped the sword. The sword was gripped like a rapier: index finger over the crossbar, and thumb on the back of the ricasso.
The cut-and-thrust sword, and the style of swordplay that one employs with it, is occasionally referred to in modern times as a "sidesword", a literal translation of the term spada di lato.
The sword/style are also sometimes referred to as "Bardi-sword" or (more correctly) "Dardi-sword" for the name of the legendary master whose students in Bologna were Marozzo, dall'Agocchie, and their ilk.
Like the longsword and unlike the rapier, the cut-and-thrust sword was commonly used in melee situations, rather than mainly as a dueling weapon. It was the standard sidearm of pikemen all across Europe in the sixteenth century; it would be used when the enemy breached the line of pike, rendering the polearm useless; this is the original of the name "sidesword". However, like all swords, it would also have been used in dueling situations.
All good masters taught that the single sword should be practiced before learning to fight with multiple weapons. The sidesword was most commonly used with a shield (a targa or buckler, typically), but it could also be used with a dagger, cape, or in a case of swords.