An offshore universal riser system may include a valve module which selectively permits and prevents fluid flow through a flow passage extending longitudinally through a riser string. An anchoring device may releasably secure the valve module in the passage. A method of constructing a riser system may include the steps of installing the valve module in the passage, and installing at least one annular seal module in the passage. The annular seal module may prevent fluid flow through an annular space between the riser string and a tubular string positioned in the passage. Drilling methods may include injecting relatively low density fluid compositions into the annular space, and selectively varying a restriction to flow through a subsea choke in a drilling fluid return line. The riser string, including housings for the various modules and external control systems, may be dimensioned for installation through a rotary table.