Many polar molecules and ions cannot cross a lipid bilayer rapidly on their own. Membrane transport proteins provide selective pathways through the hydrophobic membrane interior.

Two major classes are channels and carriers.

Channels

A channel protein forms a hydrophilic pathway through the membrane. When the channel is open, selected solutes can move through without binding and being transported one molecule at a time.

Channels can be highly selective. An ion channel may discriminate among ions by pore size, charge and the chemical groups lining the pore.

Many channels are gated: they switch between states with different probabilities of being open. Gating can respond to an electrical potential difference across the membrane, binding of a signaling molecule, mechanical force or other signals.

Aquaporins are channels specialized for rapid water transport.

Carriers

A carrier or transporter binds one or more solutes at a specific site, changes conformation and releases the solute on the other side of the membrane.

A simple alternating-access model is:

outside-facing → solute binds → conformational change → inside-facing → solute released

The binding site is not continuously open to both sides at once.

Because carrier transport requires binding and conformational cycling, it can become saturated when nearly all carriers are occupied and cycling as rapidly as they can. Channels can also have finite throughput, but they do not use the same one-binding-site-per-transport-cycle mechanism.

Selectivity does not determine direction

A channel or carrier can be selective for a particular solute without actively forcing that solute in one direction. Direction depends on the solute's thermodynamic driving force and, for active transporters, on any coupled energy source.

Thus channels and carriers solve the permeability problem by providing controlled molecular pathways. Whether transport is passive or active is a separate question about what drives movement through those pathways.