Modern society is characterized by the use of information and communication technologies. Older adults are believed to face challenges while learning to use new technologies but there is very limited understanding of what those challenges are or how they should be overcome. In this paper, we present findings from a literature review of 22 articles conducted to a) identify challenges that older adults face learning digital skills, and b) understand older adults' reactions in response to learning challenges. The findings indicate that older adults mainly face five types of challenges in learning digital skills: 1) age-related barriers, 2) problems related to technology features or design, 3) perceptions of low self-efficacy, 4) negative societal attitude, and 5) complexity of training materials. The findings also indicate that facing and trying to overcome the challenges result in negative emotions like fear and anxiety which are detrimental to gaining confidence in technology use. We identify opportunities to improve digital skills training so that older adults can benefit from confident use of new technology.