The vast majority of neural processes (and their associated mental processes) in the brain are subconscious (or unconscious), i.e. we are not consciously aware of them and cannot consciously control them. Yet, without these subconscious processes, we will not be able to live as we do now – we will have to spend an incredible amount of time and effort to consciously control all the processes that are naturally subconsciously controlled now. As a matter of fact, we will not be able to consciously do such tedious yet demanding tasks well, and we will die.
All neural processes except the final-stage sensory perception neural processes and the highest cognitive neural processes are subconscious. The subconscious neural processes are in all parts of the brain:
Brainstem and autonomic system. For example, neural processes that control breathing, heart contraction, pressure in the arterial and venous systems, body temperature, sleep-wake cycle, secretion of various body fluids (sweat, tear, saliva, gastric juice, etc.), secretion of various hormones, various reflexes (pupillary light and accommodation reflexes, optokinetic reflex, vestibulo-ocular reflex, etc .), homeostasis of various blood constituents, etc.
Cerebellum. For example, neural processes that control contraction & movement of hundreds of millions of muscle fibers of various agonist and antagonist muscles for balance and accuracy in walking, writing, speaking, playing various sports, playing various musical instruments, etc.
Deep cerebral nuclei. For example, neural processes that control the tone of your trunk muscles (when sitting, standing, walking, etc.), emotion (*1), formation, storing, and retrieval of memory (*2), etc.
Cerebral cortex. For example, neural processes that perform early-stage sensory perception (*3), early-stage language functions (*4), some stages of decision, some forms of thinking (*5), etc.
And, if you include spinal cord, the majority of their neural processes are subconscious too.
N.B.
*1. That's why we can't completely control our emotions at will: we can't get out of anger, sadness, depression, etc. or get into any emotion we want instantly at will, because they are partly controlled by subconscious neural processes. Also, we will not be able to have any emotion even if we try to if the subconscious neural processes (in the amygdala and other nuclei in the limbic system) for emotion are impaired (such as in various apathy disorders: Alzheimer’s disease, Parkinson’s disease, fronto-temporal dementia, etc.)
*2. That's why you can't memorize new events or recall past events, even if you try, if the subconscious neural processes (the hippocampus and other nuclei in the limbic system) that form, store, and retrieve memory are impaired.
*3. That's why we can't consciously see in colors (achromatopsia), can’t recognize familiar faces (prosopagnosia) (including one’s own face), or can't recognize what the object is (visual agnosia) if the subconscious processes that process color, object identification, or face identification are impaired.
*4.That's why we can't understand what people say even if we hear them clearly (sensory dysphasia) or can't understand what the text in the book means even if we see it clearly (alexia) if the subconscious neural processes that processes the meaning of the sound or of the image is impaired.
*5. See more details in the references below.
References.
General, basic information about unconscious processes in the brainstem, autonomic nervous system, cerebellum, and deep cerebral neuclei (basal ganglion, thalamus, amygdala, etc.) can be found easily by searching the internet.
Some of the more in-depth, interesting articles about this matter are as follows (and more references can be found inside these articles):
Bargh JA, Morsella E. The Unconscious Mind. Perspect Psychol Sci. 2008 Jan;3(1):73–79. DOI: 10.1111/j.1745-6916.2008.00064.x.
Dehanene S. Fathoming unconscious depths. In: Consciousness and the brain. Penguin Books. 2014. New York, New York, USA. ISBN 978-0-670-02543-5, 978-0-14-312626-3. p 47-88.
Dijksterhuis A. First neural evidence for the unconscious thought process. Soc Cogn Affect Neurosci. 2013 Dec; 8(8): 845–846. doi: 10.1093/scan/nst036.
Dijksterhuis A, Strick M. A Case for Thinking Without Consciousness. Perspect Psychol Sci. 2016 Jan;11(1):117-32. doi: 10.1177/1745691615615317.
Hallett M. Volitional control of movement: The physiology of free will. Clin Neurophysiol. 2007 Jun;118(6):1179–1192. DOI: 10.1016/j.clinph.2007.03.019 PMCID: PMC1950571 NIHMSID: NIHMS24077.
Horga G, Maia TV. Conscious and unconscious processes in cognitive control: A theoretical perspective and a novel empirical approach. Front Hum Neurosci. 2012; 6:199. doi: 10.3389/fnhum.2012.00199.