Verilog and VHDL are hardware description languages used to design digital circuits. Verilog was developed starting in 1985 and became an IEEE standard in 1995. VHDL was developed for the US Department of Defense starting in 1981 and also became an IEEE standard. Both languages use syntax similar to C and allow designers to describe circuits at different levels, from behavioral to structural descriptions using logic gates and modules. They support data types like nets, registers, vectors, and integers to model hardware. Common constructs include modules, ports, continuous assignments, procedural blocks, and instantiating lower-level modules.