We present a theory for the irreversible adsorption of semiflexible polymers, described as worm-like chains (WLC) of persistence length and contour length S, from dilute solution, with a focus on chemisorption (reaction limited adsorption). Early stages are dominated by single chain adsorption. For stiff to moderately flexible chains, shorter than S*∼ 5/3/b2/3 with b the monomer size, adsorption proceeds out of the first binding point with minimal, flat, adsorption loops of size so ∼ 1/3 b2/3 by simple zipping in S/s0 steps. For more flexible chains obeying S > S*, adsorption proceeds by multiple zipping from several nucleation points distant along the chain. At a certain typical surface concentration, larger than the 2-d overlap concentration, steric hindrance between incoming polymers and those lying already flat on the surface becomes relevant. The interfacial profile built by stiff loops dangling in the solution comprises an inner layer and an outer layer, where the concentration decreases with the distance z to the surface as ∼1/z and ∼1/z2, respectively. This is in contrast to the ∼1/z4/3 profile predicted for reversible WLC adsorption. The last distant adsorption spots are filled by end grafted chains. We also provide typical adsorption times and a short discussion of physisorption.