Why are modern aircraft wings often pointed instead being more rectangular?
Rectangular wings are easy to build: You need just one rib size and can repeat making it several times, using the same jig. Early airplanes needed a lot of manual assembly by semi-skilled workers, and it made sense to simplify the task.



SE5a wing under construction (picture source)

However, to produce the least amount of induced drag, the downwash behind the wing should have the same angle over the whole wingspan. This can be achieved with washout, but then the washout needs to be tuned to one angle of attack. Change the angle of attack and your lift distribution over span is producing more drag than necessary. To overcome this problem, elliptic wing planforms were used, but they are complicated to build and prone to tip stall. This is when the wing tip loses lift first during a stall and causes the aircraft to roll violently. If this happens close to the ground, a crash is inevitable.

Therefore, designers soon settled for something wich resembles the elliptic planform, but leaves more area at the tip such that it has less loading and more stall margin. Especially when this wing is covered with sheet metal, it makes sense to have only one direction of curvature, thus trapezoidal planforms soon became the preferred way of building wings once aluminium became the primary structural material for aircraft.



The SB-11 glider uses a rectangular inner wing and a trapezoidal outer wing. This way, the mould for the inner wing could be used for the left and right side, making construction easier (picture source).

The trapezoidal wing is also helpful in another respect: Cantilever designs have high bending moments at the wing root. If the root has more chord, the spar can be made thicker, and if the area at the tips is smaller, less bending moment is created for the same lift. The bracing of biplanes takes care of root bending moment, but when monoplanes emerged, the rectangular wing lost most of its benefits.

Now for the rounded wingtips: They are an attempt to get the wing closer to the ideal elliptic planform without losing the benefit of a constant-chord wing over most of the span. Much of the wingtip design is also about aesthetics, and some people hold quasi-religious beliefs about the benefits of a particular wing tip shape. For metal wings, wingtips can be made by pressing the aluminium sheets for the top and bottom part in shape and riveting them together since the aerodynamic loads on the wing tip are low. Wingtips and fairings were also among the first parts on aircraft to be made with composite materials, which make three-dimensional shaping much easier. Closer to the root the wing needs much more strength, and here the trapezoidal planform is still the best compromise today.