This paper briefly presents some aspects related to the way banks may use digital and social technologies to enhance their customer engagement and loyalty. In the first part of the paper we realized a brief introduction related the current developments of the banking sector related to adoption of mobile technologies and social media, the evolution from transactional banking to relationship banking. In the second part of the paper we emphasize the role of social analytics capabilities (social Customer Relationship Management systems), alternative distributions channels and other dedicated marketing activities over an efficient growth of the banking sector. The third part of the paper presents what social media represents for banks, its main advantages and challenges, providing solutions for managing weaknesses and building on strengths. The paper ends with conclusions related to the challenges existing in the banking sector and to the manner in which digital and social realm shape current banking practices and future opportunities for the banking sector, preventing banking business models become obsolete.