Cylindrical and conical surfaces are examples of developable ruled surfaces. By unwrapping such surfaces onto a plane, planar curves are obtained from curves lying on these surfaces which are interesting not only geometrically, but also in practical applications. This paper presents some methods of description and numerous examples of curves obtained by unwrapping lateral surfaces of cones and cylinders. A curve on the cylinder can be formed by cutting by a plane or another cylinder, i.e. drilling with a cylindrical drill, where drill diameter and its distance from the axis of the cylinder are varying. The typical curve obtained by unwrapping the intersection curve of the two cylinders is given by the equation of the form \(u(x,z) = p(r \sin{\frac{x}{r}}, z)\) where \(p(t,z) = 0\) is the equation of the profile curve of two intersecting cylinder. An inverse problem is also observed, namely, what kind of curve is obtained by wrapping onto a cylinder, such as a circle, on a cylinder curve, depending on the radius of the circular cylinder intersection. Such examples often appear in applications in construction and mechanical engineering. When studying curves formed by unwrapping of conical surfaces, it is appropriate to apply a polar coordinate system and so-called ceiling projection and umbrella transformation. In addition to general curves on the cone, curves obtained so that a conic from one cone is wrapped onto another cone or unwrapped onto a plane have also been taken into consideration. Curves obtained by unwrapping onto a plane are shown to have polar equation of the form \(R(\theta)=\frac{R_0}{1+ \lambda \sin {(k \theta)}}\) and therefore are called generalized conics. At the end, some of the most interesting examples of generalized conics are shown.