Since the great financial crisis, monetary policy has experienced fundamental changes and challenges. The collapse of Lehman Brothers in 2008 constituted a shock to the financial system that forced central banks to conduct policies unprecedented in scope and substance. The European Central Bank (ECB) lowered key interest rates consecutively to zero and even into negative territory for its deposit facility, provided substantial reserves to banks via targeted long-term refinancing operations, and massively increased its balance sheet via large asset purchases. Besides these economic developments, technological innovation and the appearance of cryptocurrencies led central banks worldwide to study and prepare the issuance of CBDCs. In this dissertation, I specifically address and study three of the novel features in the euro area within model-theoretical frameworks: the rise of so-called TARGET2-imbalances due to sudden stops in capital flows during the sovereign debt crisis, CBDCs and their effect on the financial system, and the vast accumulation of excess reserves as a result of the ECB's asset purchases. Chapter 1 studies the effects of a reversal in capital flows during the onset of the financial crisis. The analysis focuses on euro area periphery countries' access to the TARGET2 mechanism that allows for the substitution of private capital outflows with public inflows through commercial bank refinancing at the ECB. It applies an estimated two-region DSGE model to examine the influence of TARGET2 on credit and capital channels of core and peripheral euro area countries and to capture potential interregional feedback effects. The analysis examines how the liquidity provision to peripheral banks by the Eurosystem affects cross-border capital flows, giving rise to divergent developments across the two regions: In the periphery, TARGET2 liabilities mitigate the effects of a sudden stop and private deleveraging for consumers. Beneficial terms of trade shift household consumption to the periphery region while their output and labor decline. Core countries increase their exports and thus labor input and production while import demand decreases due to higher savings. Additionally, the distributional effects of the TARGET2 payment system lead to persistent external imbalances and real exchange rate misalignments between the regions. Chapter 2 focuses on CBDCs and studies their effects on the financial sector and monetary policy. While CBDCs might offer several benefits for users, they could potentially disintermediate commercial banks and facilitate bank runs since CBDCs, in contrast to commercial bank money, constitute digital forms of central bank money with marginal risk. Unlike cash, CBDCs presumably do not impose increasing storage costs and could therefore be used as a large-scale store of value when interest rates are low and financial distress increases the perceived risk for bank deposits. Thus, in times of financial crises, private agents could decide to convert substantial amounts of commercial bank money into CBDC, thereby posing a risk to banks' liquidity. The chapter presents a New Keynesian dynamic stochastic general equilibrium model to analyze these concerns in the absence of any CBDC-specific empirical data and simulates the effects of a financial crisis in a world with and without CBDC. In particular, it compares the effects of interest-bearing and non-interest-bearing CBDCs. The analysis shows that CBDCs indeed crowd out bank deposits and negatively affect bank funding. However, the central bank can mitigate this crowding-out effect if it chooses to either provide additional reserves or to disincentivize large-scale CBDC accumulation via low or potentially even negative interest rates on CBDC. Thus, the results suggest that a CBDC does not necessarily impair the financial sector if the central bank chooses adequate design and policy measures. Chapter 3 focuses on the ECB's large-scale asset purchases, which led to the substantial accumulation of excess reserves in the banking sector. This chapter presents a DSGE model based on Gertler & Karadi (2011) that captures the connection between a central bank's asset purchases and involuntary excess reserves in the banking system. With a substantially reworked financial sector that resembles the two-tier banking system in the euro area, the model explicitly accounts for the accumulation of involuntary excess reserves as a result of quantitative easing (QE). With additional reserves in the banking sector, banks could increase their loan supply, thus affecting the quantity of money in circulation and creating upwards pressure on prices. However, banks are restricted in their loan issuance by capital requirements regulation and low loan demand when the economy is sluggish. Assuming that the central bank uses a Taylor-rule type interest rate for its deposit facility, excess reserves do not impair monetary policy pass-through and do not pose a threat to price stability even when economic conditions improve and loan demand rises. The level of reserves does not affect optimal bank behavior. Instead, banks' loan supply is primarily determined by the interest rate margin, which the central bank can effectively steer with its deposit facility rate. Additionally, the presence of excess reserves does not necessarily impinge on bank profitability unless in times of negative interest rates with a binding effective lower bound (ELB) on deposit interest rates.