This work presents the complete general features of a recently proposed class of leaky-wave antennas, derived from stepped rectangular-section waveguides with radiating slits. Based on very favorable topological features, straightforward but extremely effective design procedures are shown to be possible for achieving sophisticated radiation properties. Furthermore, new possibilities are considered as concerns in both the use of linear arrays to scan in two dimensions, and in the introduction of dielectric parts to improve the angular pointing range and to also protect the radiating elements. The analysis of all these properties illustrates very attractive characteristics and perspectives for this type of antenna which can profitably find applications both at microwaves and at millimeter waves.