"Why would someone want to create a web of crippling anomalies?"
The Delphic Expanse spheres were a series of artificially-created spherical objects that were scattered around the Delphic Expanse. The spheres, each one nineteen kilometers in diameter, generated massive amounts of gravimetric energy and were collectively responsible for the web of spatial anomalies which constituted the Expanse. Each sphere was surrounded by a cloaking barrier which kept it hidden from outside observers. According to the Xindi-Primate Degra, the Xindi knew of seventy-eight spheres, at last count. (ENT: "The Forgotten")
Starfleet first encountered the spheres in 2153, when Enterprise entered the Expanse in search of the Xindi. The first sphere they came across was being used as a base for Osaarian pirates. Enterprise engaged in battle with an Osaarian vessel within the cloaking barrier of the sphere, and was able to take a series of detailed scans. Quantum scans of the sphere indicated it was nearly one thousand years old. (ENT: "Anomaly (ENT)")
Upon further investigation, the Enterprise crew was able to determine that the spatial anomalies which riddled the Expanse occurred at points where the waves of gravimetric energy were being emitted from the intersected spheres. This led T'Pol to hypothesize that the spheres were created for the express purpose of creating the Expanse.
The Triannon Religion
Enterprise later encountered the Triannons, who held that supernatural beings whom they referred to as "the Makers" had created the spheres to reconfigure space in preparation for their eventual return. The Enterprise crew later discovered that the Triannon myth was based in fact and that the spheres had been created by a race of trans-dimensional beings who were attempting to make the Expanse habitable for their species as a prelude to invasion. (ENT: "Exile", "Chosen Realm", "Harbinger")
A Possible Future
Captain Archer learned from Daniels, a temporal agent from the 31st century, that, in the 26th century, the Expanse would grow to encompass fifty thousand light years of the Milky Way Galaxy, and that the Sphere-Builders were trying to manipulate the Xindi into destroying Humanity in an attempt to prevent the founding of the United Federation of Planets, which would ultimately defeat the Sphere-Builders. With this information, Archer was able to form an alliance with some of the Xindi against the Sphere-Builders. (ENT: "Azati Prime")
The crew learned from Degra that the spheres were controlled by a network of artificial intelligence, and that each sphere held a redundant memory core. A team from Enterprise was able to gain access to the interior of a sphere through an exhaust port which was holographically disguised. The team was successful in retrieving the memory core, but not before Corporal Hawkins was killed by an automated defense system. (ENT: "The Council")
With the information retrieved from the memory core, T'Pol was able to determine that each sphere was connected by an interspatial manifold on its surface, and that four of the spheres were integral to the connection. Enterprise was able to disable the manifold of the sphere designated "Sphere 41" with a deflector pulse, causing a chain reaction resulting in the destruction of the entire sphere network, and eliminating the spatial anomalies in the Expanse. (ENT: "Zero Hour")
Spheres encountered by Enterprise
Scripting the spheres
In the first draft script of "Anomaly (ENT)", a Delphic Expanse sphere was said to be ninety kilometers in diameter rather than nineteen. In the first draft and final draft of the same script, the first description of a Delphic Expanse sphere's exterior referred to it as "a large, gleaming, METALLIC SPHERE the size of a small moon." In the final draft script of "Exile", the exterior of another sphere was initially described in much the same way as that of the first sphere, except it was referred to as "giant" rather than "large". The same script additionally described the exterior as "sleek" and "a vast, gleaming, metallic landscape with a mild but noticeable curvature." In the final draft script of "Chosen Realm" (which was initially called "Untitled Sphere Story"), another of the spheres was described as "vast, metallic, mysterious, hanging in space."
The interior of the sphere, in the final draft script of "Anomaly", was described as a "dark, cavernous interior" which was absolutely enormous and "easily spans a major metropolis." The script continued, "At the CENTER of the Sphere, we see an assembly of SEVEN exotic, high-tech STRUCTURES that tower outward in various directions. Only three of the towers are ACTIVE, PULSING with POWER like some kind of skyscraper-sized nuclear reactors; the other four are dark, inactive. A deep, percussive RUMBLING sound echoes through the interior."
Illustrating the spheres
The usual appearance of a Delphic Expanse sphere's exterior was designed by production illustrator John Eaves. He drew a total of six concept sketches before the fourth one was approved. The first of these proposed designs was heavily influenced by the look of an unapproved initial design for the Suliban helix, illustrated earlier in the series run of Enterprise. "The first drawing of the sulibon [sic] helix ship had this sphere drawn in as the core of the ship," recalled Eaves. "When it came time for the xindi sphere's to go in for approval I borrowed the sulie core and offered it as a choice." The sketch for the sphere even had a massive opening that, in the original Helix design, had been intended to allow access for Suliban cell ships. 
The sphere's interior was designed by Doug Drexler. He later explained that an early digital concept painting for the sphere's innards had "a more linear and 'constructed' looking central core" than the final design, which instead looked as if it had been grown. Not only was the accepted design generally approved but Drexler himself preferred it. "Frankly, I really wanted to do the organic looking one because it reminded me of Vgr," he reminisced. After being given the go-ahead, the digital artwork was delivered from the art department to Eden FX, by whom it was then adapted for television usage. Drexler also created a cutaway view of a sphere, showing the seemingly organic interior beneath a portion of the sphere's outer skin.
Visualizing the spheres
The Delphic Expanse spheres were visualized almost entirely with CGI. Green-screen was used for some shots of environmental suited Enterprise crew members walking on one of the spheres. "Their entire environment is created by us. There's nothing practical," explained Director Roxann Dawson, during production. "It's all created by visual effects. So, in order to do that, it has to be planned with everyone in mind, so that we all know what we're doing on shots like that." ("A Day In The Life Of A Director – Roxann Dawson ", ENT Season 3 DVD special features) For foreground portions of a sphere's interior in the episode "Countdown", large metallic-looking set pieces were reused, having been created for the earlier season three installment "The Forgotten" to represent parts of Enterprise's hull. The pieces were re-detailed for their inner-sphere usage and later went on to be included in the interior set for the Xindi weapon. (Star Trek: Communicator issue 151, p. 59)