A method of drilling and completing a wellbore in a geological formation to produce hydrocarbons from a well comprising at least the following four steps: drilling the well with a retrievable drill bit attached to a casing; removing the retrievable drill bit from the casing; pumping down a one-way valve into the casing with a well fluid; and using the one-way valve to cement the casing into the wellbore. Other methods are described to drill and complete wellbores in a geological formation with different types of pipes following the removal of retrievable, or retractable, drill bits from the pipes by using pump-down one-way valves.