In the above picture, if the offensive player (in white) catches the disc, he will be Out of Bounds. Why? The perimiter lines are not part of the playing field proper, and he's sitting on the line (you can see the cones behind him). The disc is on the in-bounds side of the player. The line in this case is a Port-A-Field. It's plastic, and as played at Potlatch 2003, is as straight and accurate as any line previously made with chalk or paint. If there are no lines, the space between the cones is considered the perimeter line.
The first point of contact determines whether a player is in-bounds or not. In this case, this player's point of contact includes all body touching the ground. If a player has multiple points of contact (both feet down), all have to be ENTIRELY in-bounds for the player to be in-bounds.

What happens when the player is out of bounds as they catch the disc, or as the first point of contact after catching the disc? If the player is offensive, it's a turnover.

Can a player with the disc be out of bounds and still retain possession? There are three reasons this could happen.

a player, whose first point of contact is in bounds after catching a disc, is then taken out of bounds by their momentum, retains possession but must return to the playing field to throw the disc.

a pivoting player may contact the out of bounds (assuming that their pivot foot remains in contact with its original position). It is common practice that a pivot foot ON the out of bounds line is considered in bounds. So, while technically that foot is OUT OF BOUNDS, since it is their pivot foot, the player is still considered in bounds.

if a player who catches the disc is contacted and forced out of bounds by another player prior to landing, they can call a foul and retain possession . This rule is a bit ambigous, as it is unclear what happens if the player is fouled PRIOR to posession.

If an offensive player's last point of contact is out of bounds prior to receiving a disc, and they land in bounds, what is their status? Out of bounds.

What is controversial about inbounds/out of bounds calls?
According to the rules, the player with the best perspective determines whether a player is in or out of bounds. As played, there is often contention about which player has the best perspective. As often played, the receiver is thought to have the best perspective even if this is not the case. As almost all ON FIELD parties have a VESTED INTEREST in the call, it is not uncommon for the two teams to disagree according to the line that benefits them. It is NOT UNCOMMON for out of bound players to call themselves in bounds (and for that call to stand), nor is it exceptional for a player to land out of bounds and play on as if nothing had happened (it is difficult for the defense to call this). Of course, in bounds players are also sometimes called out of bounds. When observers are used, they sometimes make active Out of Bound calls. This is an improvement over self-calls.