Status of top quark searches at hadron colliders and present mass limits.

We discuss the present top quark searches and lower limits on the top mass from the CERN and Fermilab collider experiments, and what may be expected from the latest data-taking periods of 1988/89. Since with the data of 1989, the mass domain probed should extend up to mt ∼ mW, we discuss some aspects of this t-quark mass range, some experimental hints, and the background of W + ≥ 2 jet events.