Tumour recurrence is one of the biggest challenges in breast cancer management because it affects 25-30% of women with breast cancer and the tumours are often incurable. Women with triple-negative breast cancer (TNBC--lacking expression of the oestrogen receptor, progesterone receptor and the receptor HER2/ERBB2) have the highest rates of early recurrence relative to other breast cancer subtypes. Early recurrence might be due to tumour-initiating cells (TICs), which are resistant to conventional therapies, can remain dormant and can subsequently give rise to secondary tumours. In breast cancer, TICs are identified by the cell-surface markers CD44+/CD24-/EpCAM+ and/or possess ALDH1 enzyme activity. This subpopulation has the ability to self-renew, grow as mammospheres and initiate tumour formation. Fuelling the problem of relapse is the fact that chemotherapy and radiation can induce or select for TICs; this was reported in preclinical models and more recently in women being treated for breast cancer. Thus, new therapeutic agents for TNBC are presently being sought to overcome this problem. Here we review the roles of receptor tyrosine kinases, signalling intermediates and transcription factors in sustaining the TIC subpopulation. Particular emphasis is placed on targeting these molecules in order to eliminate and/or prevent the induction of TICs and ultimately reduce the frequency of TNBC recurrence.