We present detailed experimental and theoretical results on population transfer with frequency-swept picosecond laser pulses. Here, we demonstrate that intense frequency-swept pulses, when applied in the adiabatic limit, lead to both more efficient and more selective excitation than do unmodulated laser pulses. The experimental work is performed on quasi-two-level systems (pentacene/p-terphenyl crystal and Na vapor), quasi-three-level systems (Na vapor), and on more complex multilevel systems (I-2 vapor). We discuss the different characteristics of adiabatic population transfer in both few-level, and multilevel cases, and, in particular, present computer calculations to explore the effects of molecular rotations in multilevel adiabatic population transfer.