We present an overview of corporate-finance models where firms are subject to exogenous market frictions. These models, albeit quite simple, yield reasonable predictions regarding financing, pay-outs and default, as well as asset-pricing implications. The price to pay for the said simplicity is the need to use non-standard mathematical techniques, namely Singular and Impulse Stochastic Control. We explore the cases where a firm with fixed expected profitability has access to costly equity issuance as a refinancing possibility, and that where issuance is infinitely costly. We also present a model of bank leverage.