Answer
In the classic view, glia are primarily "support cells" that handle non-computational affairs in the brain: clean-up and maintenance, immune responses, etc.
Recent work has found that some glia, especially astrocytes, are capable of releasing neurotransmitters and other biologically-active small molecules through a process called gliotransmission.
A role for glia in computation is still unclear and controversial, but evidence is mounting.
The Classic View: Division of Labor
Until at least the 1990s, the unchallenged orthodoxy divided the cells of the brain into two basic classes: neurons, which took in information, computed on it, and produced behavior, and the glia, which served to support neurons in this endeavor. Even the name "glia" reflects this view: etymologically, the cells are simply glue that holds the brain together.
The glia are further subdivided based on gross morphology and functional role. The main classes are discussed below.
Astrocytes
Named for their star-like shape, the astrocytes have traditionally been assigned the role of "chemical janitors". They help clear the synapse of neurotransmitter following synaptic transmission, thus ensuring the timely termination of neuron-neuron signaling. They also monitor the concentrations of the various ions of the cerebro-spinal fluid, keeping them within the ranges required for neurons to have the right electrical properties.
Microglia
These tiny cells are similar to the macrophages of the immune system. They identify cell debris, usually from injuries, and foreign elements like bacteria and and consume the offending material through phagocytosis. Unlike all other cells in the brain, microglia are mobile: they can stalk and track their microscopic prey or rapidly mobilize to the location of an injury.
Myelinating Cells
In order to improve the speed of action potential conduction, the axons of neurons are wrapped in many layers of phosophlipid bilayer, commonly known as myelin. This sheet reduces the capacitance of the membrane, thus reducing the time constant for for voltage changes and signal transmission.
In the central nervous system, the glial cells known as oligodendrocytes mediate the myelination process. Each oligodendrocyte provides some amount of myelin to several neurons. In turn, each neuron is myelinated by several oligodendrocytes.
In the peripheral nervous system, glial cells known as Schwann cells serve this function. Unlike oligodendrocytes, Schwann cells mate for life, so to speak, with a single neuron, providing myelination for one segment of one axon.
Anatomical and functional differences between these myelinating cells are though to underlie the differential capacity for healing between the peripheral and central nervous systems.
A New View: Astrocytes as Integrators
Recent work has done much to challenge this conventional view of the division of labor in the brain. In particular, experimental work has emerged positing an important role for astrocytes in learning and computation. Despite its ludicrous title, one good resource for information on this topic is the review article Gliotransmitters Travel in Time and Space, by a collection of champions of the downtrodden glia.
In the tripartite synapse model, astrocytes wrap around the presynaptic and postsynaptic terminals, both shielding the synapse from external chemical influences and allowing the astrocyte to integrate presynaptic and postsynaptic signals. Because astrocytes are linked by gap junctions, networks of astrocytes can integrate this information over large distances – hundreds of microns or more. This communication occurs in the form of traveling, transient increases in intracellular calcium, also known as "calcium waves", that can be observed using calcium fluorescence imaging.
These increases in calcium mediate the release of small, biologically active molecules. This process is called "gliotransmission" by analogy to the more well-known process "neurotransmission". Some gliotransmitters are also neurotransmitters, like glutmate, while others, like ATP, are not classical neurotransmitters. Curiously, one of the most prominent gliotransmitters is D-serine, the only biologically active "right-handed" amino acid.
Calcium-mediated gliotransmission can occur via the same mechanisms as calcium-mediated neurotransmission: calcium-sensing proteins activate the SNARE complex of proteins, which cause the exocytosis of vesicles containing the gliotransmitter. Alternatively, gliotransmission can occur by a process that is literally the reversal of the neurotransmitter reuptake process: reuptake proteins are modifed by a calcium-dependent regulatory process and begin to run in reverse, spewing transmitter back into the synapse.
In both cases, astrocytes appear to be modulating homeostatic processes and gain, and possibly even the function of the NMDA receptor, which is critical for learning and memory. The exact connection between astrocytes and computation is controversial, but its existence is the result of a simple application of molecular and cellular biology's version of "Murphy's Law": "anything that might contribute to a process, does contribute to a process".