In positron emission tomography (PET), a quantitative reconstruction of the tracer distribution requires accurate attenuation correction. Attenuation correction is usually based on information obtained from transmission tomography (CT) or from MRI. We will discuss situations where such a direct measurement of the attenuation coefficient of the tissues is missing or unreliable due e.g. to patient motion between the CT and PET scans. Methods to simultaneously estimate both the tracer distribution and the attenuation using only the emission time-of-flight (TOF) PET data will be presented. These methods rely on the range condition for TOF-PET, which generalizes John's partial differential equation for the 3D x-ray transform. Using this range condition, we will demonstrate that the attenuation is determined by the TOF data except for a global multiplicative factor. Next, we will describe two monotonic iterative algorithms to approximate the maximum-likelihood estimator of the tracer distribution. Issues related to the scatter background will be discussed in this context. Finally, a few examples with simulated and patient data will illustrate the properties and limitations of this approach and its potential applications.